Parallax Markets — Lab Book

1. Path B (PRICE-ONLY) — CLOSED: rediscovery of idio-vol

Scope: this section is the FAILED first construction — five reads, all transforms of the price surface, violating the instrument's independence requirement. Its verdict is price-only. The live result (multi-family Ω) is §2 onward; do not read §1 as the global verdict.

Price-only verdict (CLOSED): the five-price-read construction spans to the idiosyncratic-volatility / low-risk anomaly (zero alpha) — a reconstruction of a known effect. This is a real but known effect, and it is NOT the document's finding; it is the failure that motivated the independence correction in §2.

2. The dig — disagreement across independent families

The price-only reconstruction failed because its five reads were transforms of one surface (price), violating the instrument's independence requirement. The dig rebuilt disagreement across independent data families with low observed correlation (mean |corr| 0.12 — non-redundancy, not proven informational independence) — price, fundamentals (gross profitability, ROA, earnings momentum, sales growth, accruals, asset growth, value), institutional 13F flow, and insiders. Gross profitability alone survives real controls (FM t=4.77); "everything is idio-vol" is false.

3. Adversary — attacking the load-bearing claim

The dose-response was, at first, reported as a monotone sequence and believed, with no adversary — a violation of this program's own audit standard (a build fails if the load-bearing claim never survives an attack). Four attacks (adversary.py):

What the adversary changed: the dose-response is real (survived every attack). The first read of the last test — "idio-vol correlation rises with rooms → mixture, not a coordinate" — was itself over-deflated. Measuring the two spaces separately:

Interim reading (superseded below): at this stage the characteristic looked largely orthogonal to the standard tested factors, and the selected-room dose-response was real relative to its placebo — so it appeared a coordinate candidate. The MSQ and geometry tests below change that interpretation. "Validated," reflexivity, and the "mixture/not-a-coordinate" over-correction were withdrawn here.

The energy-inclusive completion — disagreement vs extremeness

The "distinct at anomaly-grade strength" reading survived a complete accepted model (each characteristic vs all others, calibration twins) — Ω at t=3.7, mid-pack. But that model lacks a multi-signal-extremeness term (MSQ = mean-squared read level). Var = E[x²]−E[x]², so dispersion hides an energy component. Adding MSQ:

MSQ crushes Ω specifically (t -3.7→-1.9, below significance) while every accepted twin is unchanged or STRENGTHENS. So MSQ is a legitimate priced control, not an over-fit, and Ω's distinctness from known anomalies was largely multivariate extremeness. Algebraic caveat retained (Ω and MSQ mechanically entangled), but the twins-strengthen asymmetry is the real evidence.

Does the dose-response survive extremeness?

Raw climb is non-monotone over nested subsets (the clean 2.1→5.7 was partly room-selection-specific); the MSQ-residual climb is erratic and mostly weak. So the "more rooms → sharper disagreement" story is not robust as stated.

Exact geometric decomposition — the MSQ deflation was a collinear-control artifact

MSQ = x̄² + D, so the dispersion is inside MSQ: controlling for MSQ absorbs Ω near-tautologically. The clean test uses the exact geometric decomposition of read-vector magnitude: x = x̄·1 + (x−x̄·1), where the common-mode and centered-residual vectors are orthogonal, so ‖x‖² = x̄² + D exactly. Entering the scalar components jointly (they are not themselves independent — x̄² is a transform of x̄) and asking which is priced:

The priced component is the dispersion (disagreement), not the common-mode magnitude. So "it's extremeness, not disagreement" was substantially an artifact of a control collinear with Ω by construction. Corrected reading: dispersion of the standardized reads is priced beyond consensus and the standard factors. Methodological lesson: don't decompose dispersion with a control that contains it; use the magnitude = consensus² + dispersion split. (This is the correct form of the cross-domain energy test, too.)

Family-pair attribution — structure matters beyond magnitude

D = (1/2n²)Σ(xᵢ−xⱼ)², so dispersion is an aggregate of pairwise disagreements. Grouping by family (price / fundamentals / ownership-13F / insider):

Discovery-era interpretation, subsequently NOT confirmed OOS: in-sample, price↔fundamentals and price↔ownership appeared to add beyond total dispersion D. The frozen out-of-sample primary rejected this — PF/PO add nothing beyond D on untouched pre-2016 data (PF −0.65, PO −0.66, joint p=0.45). So the paragraph that follows describes the discovery hypothesis, not the confirmed conclusion; what replicated OOS is total dispersion D, not the finer cross-family structure. Caveat: positive "flips" for insider pairs conditional on D are suppression effects, not "insider disagreement predicts positively." Literature location: cross-observer dispersion is already priced (analyst forecast dispersion; RFS 2026 "Machine Forecast Disagreement," ML models as observers) — so "dispersion is priced" is not a discovery. The only non-redundant element: observers are heterogeneous data families, and the structure is price-vs-fundamental/ownership. Status: supported as structured cross-family conflict; NOT supported as investor belief disagreement (vs characteristic inconsistency) or as novel. Robustness re-runs and external validation (vs analyst dispersion / short interest, data-gated) pending.

4. What closed, and what it cost to get here

Path C (arrival ordering / the seismic θ_mv coordinate) reached t=1.97 on 230 large-cap survivors, then went to a powered null (reversal gate t=+4.34; SIGNAL t=+0.38) on the real universe. A clean death: thin-data near-misses do not survive breadth. That is the discipline working, and it is why the Path B pass is credible.

5. Chronological trail

origin (variance-of-disagreement latent in the quiver) → v1 rare-event (underpowered) → v2 vol / v3 drawdown (powered nulls, arena closed) → net research (path is the cross-section; dispersion is priced) → Path B/C on survivors (underpowered; C flickered at 1.97) → seismic timing probe (σ-moveout ⊥ vol, but payoff is cross-sectional) → Sharadar survivorship-free data → Path C null, Path B PASS + robustness + factor-zoo. Full detail in RESULTS_AND_LEARNINGS.md.

6. Scoreboard

7. Instrument & corpus

General instrument: σ(Ω) / variance of disagreement among independent reads — pathology → seismology → biomechanical → markets. Failed cross-sectional implementation: dispersion across five price transforms (momentum horizons, reversal, trend) — insufficient observer independence; rediscovered idio-vol (§1). Current implementation (the operative object): ten reads drawn across independent data families with low observed correlation (mean |corr| 0.12) — price, fundamentals (gross profitability, ROA, earnings momentum, sales growth, accruals, asset growth, value), institutional 13F, insiders. "Independent" here means independent data families, not proven informational independence — accounting reads share a corporate state; the honest hierarchy is source → family → statistical non-redundancy → observer independence, and only the middle two are demonstrated. Real-data corpus: Sharadar SEP 10-year bulk, 7,724 domestic common stocks on major exchanges, 72% delisted (survivorship-free), median ~4,242 names/month, 2016–2026. Incumbents reconstructed: absorption ratio, financial turbulence, persistent homology (ripser), HAR, short-term reversal, idiosyncratic vol.

8. Interpretation boundaries

• The price-only signal IS idio-vol. The Path B construction (five reads, all price transforms) spans to the idiosyncratic-vol factor: zero alpha (t=-0.21), idio-vol β=+0.67. That reading is closed — it violated the independence requirement and measured volatility.
• The multi-family signal survives conventional controls but does not establish a distinct disagreement coordinate. It is 82–92% unexplained by the initial tested set and survives the expanded accepted-characteristic model at t=3.7 (calibration twins strong). Q1 is DONE, not open.
• What carries the pricing is the dispersion, not the common-mode magnitude. The MSQ control (which collapsed Ω to t=1.9) was collinear with Ω by construction (MSQ = x̄²+D ⊇ dispersion). The exact geometric decomposition shows dispersion (D=Ω²) priced at t=−4.6 while common-mode magnitude (x̄²) is null (t=+0.8). Favored reading: disagreement (dispersion), stated as "priced beyond consensus and the standard factors." Supported, not confirmed — robustness attacks must be re-run on this clean object.
• The observer-count dose-response is not robust evidence of sharpening. It was not a simple dimensionality artifact (placebo flat), but nested room subsets are non-monotonic (5.2/8.5/7.4/5.5) and the MSQ-residual becomes erratic (0.0/3.1/0.6/2.2). Do not cite it as "more observers → sharper disagreement."
• Trade: "inert" was a coarse-sort artifact. The naive quintile sort is 84% factor exposure and earns no alpha — a factor-neutral construction earns +6%/yr, t=3.9, gross Sharpe 1.3. Caveat: ~⅔ is a small-cap size-interaction (within-size t=1.5), un-costed — measurement evidence, not a strategy.
• No overclaim: "validated," reflexivity, "just idio-vol" (multi-family), "mixture/not-a-coordinate," naive-sort "inert," AND "it's extremeness not disagreement" are all withdrawn. Earned statement: dispersion (disagreement) is the priced geometric component beyond consensus and the standard factors — supported, pending robustness re-runs on the clean decomposition.
• Terms: derived findings only; raw Sharadar data is a working cache, never redistributed. Personal-use license.

9. Forward queue

Corrections logged this session: "validated" withdrawn (overclaim); reflexivity withdrawn (effect intensifies, contradicting decay); "sample-bound" withdrawn as an alibi (no tradeable edge on data held, full stop). No pivot away from markets — the inquiry stays open here.

10. Status: exploratory, and the multiple-testing discount

11. Where this lands (uses) — a diagnostic instrument, not a factor

The defensible contribution is a characteristic-construction-and-interrogation method, plus a deterministic cross-source state variable — not a tradable factor (the ~6% gross stays in the measurement bucket: size-concentrated, un-costed). Plausible uses:

• Feature / ensemble audit: detect pseudo-diversity — the price-only collapse showed five "different" reads were one surface. A quant team can audit whether an ensemble has genuine source diversity or cosmetic feature diversity.
• Cross-source unusual-state flag: which firms are simultaneously off-ordinary across price, fundamentals, ownership, insiders — a research trigger (event review, special situations, risk committee), not a buy signal.
• Portfolio-construction audit: the naive-sort-inert vs factor-neutral-recovers lesson — distinguish measurement failure from portfolio-construction failure.
• Risk / state monitoring: test whether high-Ω names precede events / earnings surprises / liquidity deterioration rather than returns — a deterministic cross-source alerting idea.
• Research governance: calibration twins (run the destructive control on accepted anomalies too) and internal-algebra controls (derive the control from the instrument's own geometry) — transferable methodology.

12. Field-hygiene status (a finance referee's checklist)

Addressed: point-in-time lagging (fundamentals by datekey, 13F +50d), survivorship-free universe with delisting, microcap screen (price ≥ $5) + winsorization, block/Fama–MacBeth inference, calibration twins, internal-algebra decomposition. Pending (would matter for publication, not for the exploratory claim): NYSE breakpoints, value- vs equal-weighting, transaction costs / turnover, industry-neutralization, Newey–West / persistence-aware SEs, formal multiple-testing correction, and — the big one — a longer history than 2016–2026 (regimes matter; premia are noisy). These separate an interesting lab experiment from something a journal would accept.

13. The aggregate-hider turn — reconciliation, geometry, shape decomposition (2026-08-20)

Why this section exists. After the frozen OOS primary settled (novel beyond-D claim failed; base-D OOS-supportive), a VTL-derived question reopened the work at the methodological level, not the anomaly level: the aggregate is the hider. A scalar summary can be identical across objects generated by completely different mechanisms — two paintings both "centered" in total mass, one via counterweighted islands, one via a single central blob. D is exactly such a scalar: for a 10-read vector it is a radius from consensus, and many internal configurations sit on the same radius (e.g. [-2,-2,-2,+2,+2,+2,…] bimodal vs [-4,0,0,…] single rupture). The question: does equal aggregate D conceal distinct read-space geometries, and — separately — does the market care about the mechanism it hides?

13.1 Reconciliation — the D numbers are not a code artifact

Before trusting any of this, the base-D result was reconciled against the frozen primary with an independent estimator (reconcile_D.py). Result: no implementation discrepancy. The same estimator reproduces every reference number exactly. The earlier −3.01 for D+factors was audit_confirmation.py's plain-iid Fama–MacBeth t; applying the pre-registered Newey–West(3) to the audit's own coefficient series (imported in-memory, byte-identical rows/months) gives −2.27. The −3.01-vs-−2.74 gap is inference (iid vs NW), not the effect. A forward-return boundary leak (a diagnostic building fwd on the extended cache, letting the last month peek past the outcome boundary) was caught and fixed here.

The 25/31/47/59-month spread is mechanical: PF/PO require 13F ownership (→ 25 mo from 2013-11), D+factors requires momentum history (→ 47 mo from 2012-01), D-alone/rank-IC need only D (→ 59 mo from 2011-01). Same estimator throughout. Honest characterization of base-D with controls: −2.0 to −2.8 — real and negative, modestly weaker than the iid −3.01 implied, never dependent on any leak.

13.2 Geometry stable across eras — same measured state

Descriptive, no returns (geometry_compare.py): the disagreement geometry is nearly the same object in the discovery era (2016+) and the OOS era (2014-15).

Family-centroid correlations are near-identical across eras (price↔own +0.29/+0.26, own↔insid −0.19/−0.18, fundamentals near-orthogonal to all in both); D's month-to-month rank persistence is +0.888 / +0.896. Smallest defensible reading: same measured geometry, different predictive attribution. The OOS failure of the novel claim is not the instrument reconstructing a different cross-source geometry across eras — only the finer PF/PO structure's return association failing to replicate. No ontological "state changed" claim is warranted.

13.3 Shape decomposition — the aggregate IS a hider (descriptive, no returns)

Per firm-month, inside D, two shape axes (shape_descriptive.py, discovery 2016+, all-10-reads, price≥5, 281,538 firm-months): concentration C₁ = maxᵢ dᵢ² / Σ dᵢ² (dᵢ = xᵢ − x̄; high ⇒ one read ruptures) and polarity P = 2·min(E₊,E₋)/(E₊+E₋) (0 = one-sided rupture, 1 = balanced two-sided split); participation ratio PR reported as a descriptive companion to C₁, not a second test.

Findings. (i) C₁ and polarity collapse to one axis (corr −0.86); PR is −0.93 with C₁. So there is one effective free shape dimension — concentrated/one-sided ↔ distributed/two-sided — not five. (ii) Shape is entangled with D itself (corr(D,C₁) = +0.40): higher-D states are more rupture-like on average, so a C₁ main effect co-moves with D and the honest question is shape conditional on D. (iii) Large residual shape variation at fixed D: across mid-D deciles C₁'s p5–p95 spans ≈0.26 to ≈0.78. The geometry-only twin makes it concrete — two firms at D≈0.30: ATKR C₁=0.86, P=0.28 (a single SUE rupture at −1.69, everything else ≈0) vs MLI C₁=0.17, P=0.87 (disagreement spread across many reads in a balanced ± split). Same radius, opposite internal state. Conclusion: D is lossy about mechanism — the "D is a complete descriptor of the state" outcome is ruled out at the measurement level. What remains open is whether the market cares about the hidden mechanism.

13.4 Confound audit — is "rupture" a geometric condition or one noisy read?

Among firm-months, which read owns the maximum squared deviation (dominant_read_audit.py, no returns):

Two-part answer. Through moderate concentration (C₁ ≈ 0.6–0.7, the bulk of "concentrated" states), the rupturing read is spread across five or six channels — concentration has the same distributed character D itself has, so it is a genuine geometric condition, not a single-channel pathology. But the extreme tail (C₁ > 0.8) is confounded: insider net-buying owns 43% and sales growth another 15%, both structurally sparse/spiky reads (intermittent filings → occasional large z-scores). So the most extreme "single rupture" states are disproportionately a sparse read firing — mechanism, not signal. The shape variable is real in the mid-range; any consequence test must be robust to the tail rather than chase it.

13.5 Consequence spec (frozen) and RESULT — ran once 2026-08-20

The consequence question (does shape conditional on amount carry return consequence?) was frozen as a minimal pre-registration (PREREG_SHAPE.md, sha256 9cd845b7…; harness run_shape_consequence.py, sha256 381f9497…) and run ONCE. Per GPT's edit before the run, the primary observer system is all-10 reads (every firm-month the same ten-dimensional instrument), with ≥6/10 demoted to Robustness A; the two roles of D are documented (raw D_raw for the residualization map; z_t(D_raw) as the consequence regressor). Frozen design:

Reading (within the frozen rules, no overreach). Shape conditional on amount carries detectable incremental consequence beyond aggregate D — the aggregate is a consequential hider, robust across three geometries; the interaction is null (additive, does not scale with D). Sign: C₁_resid is positive, so at equal aggregate D the more-concentrated (single-read rupture) states earn higher returns and distributed disagreement earns lower returns. With D negative, the most negatively-priced state is high-D and distributed = broad multi-source incoherence — broadly distributed cross-read inconsistency is the state associated with the stronger negative return relation (an association, not a demonstrated economic mechanism; a latent known characteristic could in principle generate both broad read-space dispersion and low returns). This is the first NEW Parallax structural hypothesis in the markets arc to survive its frozen test (the PF/PO "beyond-D" refinement failed its frozen primary; this passed). Status: retrospective / secondary-historical-validation — meaningful corroboration of a geometry-derived hypothesis under a frozen spec, stronger than in-sample discovery, but NOT pristine confirmation (pre-2016 was already opened for other purposes). One pre-registered primary, so no forking-paths discount on +3.00; but 26 months is thin (hence the ≥6 robustness at 48 mo, +4.32, and the temporal battery in §13.7). Novelty is quarantined, not claimed: a literature audit (§13.7) finds the general "shape beyond amount" principle KNOWN (closest prior: belief-polarization, Hardouvelis-Karalas-Vayanos 2025) but locates no direct equivalent of concentration-of-heterogeneous-cross-characteristic-dispersion-conditional-on-amount. True confirmation still needs a genuinely untouched time block or the cross-domain transfer with this exact frozen spec.

13.6 Governance — pre-2016 is no longer a pristine holdout

The pre-2016 window was untouched for the original PF/PO confirmation. It has since been opened for D regressions, rank-IC, geometry comparison, and sample reconciliation. It is untouched with respect to C₁-vs-return results specifically (nobody has looked at that there), but it has already shaped our thinking about D, the controls, the samples, and the instrument. So a C₁ test there is secondary historical validation, not independent confirmation. A positive there would be taken far more seriously than another in-sample discovery, but true confirmation needs a genuinely untouched block — future accumulating data, or a cross-domain transfer with the shape hypothesis frozen before consequence is examined. Open decision (awaiting input): (a) run the frozen secondary-validation pass on pre-2016 now; (b) edit the freeze first; or (c) hold the frozen spec unrun and carry it straight to an untouched domain so its first contact with returns is the pristine one. What this turn already bought: we asked whether Markets failed because aggregate D was hiding mechanism — and we now know it is hiding mechanism; what we do not yet know is whether the market cares about the mechanism it hides.

13.7 Temporal stability + literature-location (2026-08-20)

Temporal battery (frozen PREREG_SHAPE_TEMPORAL.md, sha 43da5237…; harness run_shape_temporal.py). Instrument frozen; only time segmentation varies. The all-10 instrument needs 13F so the clean battery lives in the later era (2018-2026 effectively) with pre-2016 as the comparison block; the 2016+ C₁→return relationship had not been examined before, so it is an un-inspected reproduction, not a re-use.

Leave-one-calendar-year-out (later era): all 11 folds positive, t=+1.6..+2.8 — no single year is necessary. Rolling 36-mo path (below): near-zero in the earliest 2017-2020 windows, then climbs and holds positive from ~2020 (peak t=+2.87); no material sign reversal — one window is trivially negative (t=−0.05 ≈ 0). Headline reproduction: pre-2016 all-10 t=+3.00 → pooled later-era all-10 (2018–2026) t=+2.12 (≥6 companion +4.32 → +2.77), same sign and still significant, ~half the magnitude. (The all-10 homogeneous panel begins 2018-03-29, when the ten-read system first has 13F throughout — "later-era", not a full ten years of all-10 data.)

Verdict (against the frozen ladder): temporally supportive, regime-varying. Positive across the whole chronology with no material sign reversals (one rolling window trivially negative, t=−0.05 ≈ 0) and no single-year dependence; two non-overlapping strong periods (pre-2016 t=3.00 and 2021-23 t=3.06); reproduces significantly in the later un-examined era — so not a one-period accident. But magnitude is regime-modulated (near-zero through 2018-2021) and the thin-window +3.00 was magnitude-inflated (durable coefficient ≈ half, t≈2.1-2.8). Not a constant law, not pristine confirmation. Plain-language finding: firms with the same total cross-characteristic incoherence can reach it via one extreme signal or many jointly-conflicting signals; those states are not return-equivalent (more distributed incoherence → lower subsequent returns), and the relation recurs through time though its strength varies by regime. UNKNOWN (recorded, NOT an invitation to search): why does the C₁* consequence vary materially through time while keeping its broad sign? A thousand macro variables (rates, vol, sentiment, liquidity, COVID) offer post-hoc stories; correlating the rolling coefficient against them now would re-open the garden. It sits as an open question. This moves Markets from "instrument-validation with an interesting secondary result" to a candidate finance contribution: meaningful in-domain replication, unresolved novelty, no pristine prospective confirmation.

Literature-location (novelty quarantined). The general principle "the internal shape of disagreement matters beyond its amount" is KNOWN. Ledger:

Own forensic web check (2026-08-20), adversarial (trying to FIND the exact prior): could not locate a direct equivalent. Verified differentiators from each neighbor — Hardouvelis-Karalas-Vayanos (closest): range/kurtosis are moments of the analyst-belief distribution about one quantity, ownership dispersion is a Herfindahl of holdings breadth — neither is concentration across heterogeneous characteristics; their coordinates are homogeneous beliefs, ours are heterogeneous firm-descriptions; their shape statistic is distributional kurtosis, C₁ is one-vs-many concentration of a fixed total cross-read dispersion. Stambaugh-Yuan mispricing score = arithmetic average of 11 anomaly ranks = the consensus/mean direction — the mathematical opposite of concentration-of-dispersion. Machine Forecast Disagreement = forecast dispersion amount; no concentration/higher-moment topology test located. Huang-Li-Wang "Are Disagreements Agreeable?" = PLS aggregation of many disagreement measures to time the market — combines, does not decompose; time-series not cross-section. Cross-sectional valuation-dispersion / higher-moment work is across firms or on the return distribution, not within-firm across-reads. So ~half of D being fundamentals-vs-fundamentals, the object is best named cross-characteristic state incoherence, not "belief disagreement." Novelty: plausible but unresolved, NOT claimed. Full-text confirmation (Hardouvelis, from the source PDF): they measure polarization by the kurtosis of, in their words, "the distribution of analysts' forecasts"; range measures intensity of disagreement; the Herfindahl index is their measure of ownership breadth; kurtosis is tested conditional on range. So it is a genuine shape-conditional-on-amount precedent — but over the analyst-forecast distribution, and their kurtosis/polarization maps onto our polarity axis over beliefs, not our primary concentration (C₁) over heterogeneous characteristics. Full-text confirmation (MFD, from the source NBER PDF): MFD is defined as "the standard deviation of [return forecasts] across investors" — dispersion amount only. A term search of the full 54-page text finds no kurtosis/skewness-as-predictor, no Herfindahl/concentration/participation-ratio, no "one rogue model vs distributed," and no conditional-on-total-dispersion shape test; the robustness section varies the ML model (ridge vs random forest) and geography, not the shape of disagreement. So both closest papers are now full-text-checked and neither contains the C₁* object. Remaining honest limit: "no prior located" ≠ "no prior exists" — an exact prior could still sit under other terminology or in a non-finance/ML paper; a literature search cannot prove the negative beyond this. Structural distinction a referee can read directly: Hardouvelis = distribution of homogeneous beliefs; MFD = dispersion across model forecasts; Stambaugh-Yuan = average direction across signals; Parallax = heterogeneous descriptions of one firm → D = total cross-description inconsistency, C₁* = concentration of that inconsistency conditional on its amount.

13.8 Paper build, referee-response, and adversarial self-validation (2026-08-20)

The frozen Stage-1/Stage-2 evidence was written up as a finance manuscript (measurement/representation framing, zero Parallax vocabulary): RESEARCH_NOTE.md (~6pp), MANUSCRIPT.md (~20pp, standalone HTML with embedded figures), title "Cross-Characteristic Dispersion and the Cross-Section of Stock Returns." Table 1 = plain joint D+C₁; C₁* the estimand-clean confirmation; PF/PO the falsification box; economic magnitude via a frozen conditional sort. Two external-review rounds then materially sharpened it.

Referee-response robustness (pre-declared, run_referee_response.py). (a) Short-term reversal: momentum is 12−1 so 1-month reversal was absent from controls. Adding STR leaves the shape coefficient essentially unchanged (C₁* +3.00→+2.97 pre-2016, +2.12→+2.21 later); the effect is not reversal in disguise. (b) Value-weighted magnitude: the ≈45 bps/21d equal-weighted spread attenuates to near zero value-weighted and among liquid names (later era EW −45 → VW +11 t=+0.47; liquid-EW −6). The magnitude is a small-cap phenomenon.

Adversarial self-validation (adversary_check.py) caught an over-claim of mine. I had framed it as "the statistical association survives; only the economic magnitude is small-cap." That split was false. The Fama–MacBeth slope itself collapses in liquid names: later-era C₁* t = +0.57 on the top-half-market-cap subset (vs +2.12 full), coefficient ~¼ of full; pre-2016 liquid t = +1.65 (vs +3.00); in the small-cap half it is stronger (t = +2.14, +3.49). The STR defense, by contrast, strengthened: C₁ and STR are essentially orthogonal (cross-sectional corr ≈ 0.00–0.04), so C₁ cannot be reversal relabeled (though STR is itself weak in a ≥\$5 universe).

Honest current scope of the return finding: a small-and-illiquid-stock phenomenon in both statistical and economic form — robust in small caps (t 2.1–3.5), weak-to-absent among liquid names (t≈0.6 later), survives reversal. This is a real narrowing from the "general cross-sectional relationship" the draft implied that morning. The measurement contribution (the aggregate-hider decomposition, the descriptive-before-returns spine, the PF/PO falsification) is independent of return magnitude and unaffected.

Limits-to-arbitrage vs microstructure-artifact test (pre-committed verdicts frozen BEFORE running — PREREG_LTA.md, run_lta.py). Committed: REAL = implementation-gap survives + an arbitrage-cost support; ARTIFACT = gap collapses; MIXED = gap survives but supports fail. Result: MIXED. The gap test (primary discriminator) SURVIVES and strengthens — skipping the first 5 trading days takes later-era C₁* from t=+2.12 to +3.40 (gap coef 126% of baseline), so the effect is NOT a microstructure / bid-ask / stale-price artifact (those decay within days). But both mechanism supports fail: C₁*×IVOL interaction t=+0.76 (<1.5), and the slope does not survive excluding the bottom market-cap quintile (later t=+0.55). Committed verdict honored: a genuine, non-artifact predictive signal CONFINED TO MICROCAPS, of UNRESOLVED mechanism — NOT claimed as limits-to-arbitrage. This rules out the near-fatal "just microcap microstructure noise" possibility (a real gain for the finding's validity) while leaving it without a mechanism or large-cap presence.

Reducibility kill (cheapest-kill generator; pre-committed verdicts frozen first — PREREG_REDUCE.md, run_reduce.py). Generator: "what single result ends the claim?" → C₁* is a nonlinear repackaging of the ten reads, so adding them as linear controls should absorb it. Committed: REAL = later-era C₁* |t|≥1.5 with the ten reads controlled; DEAD = |t|<1.5 or sign flip. Result: DEAD in the primary sample. Later era (n100): C₁* t +2.12 → −0.06 once the ten reads are added (ratio −0.03). Pre-2016 (n26): +3.00 → +2.87 survives. Committed verdict (primary = later): REDUCIBLE. A relation that holds in 26 months and vanishes in 100 is not robust; honored the pre-commitment, did NOT switch to the surviving sample. So C₁*'s RETURN predictability is the reads' own linear signals repackaged through concentration, not an incremental geometric effect. This is the biggest deflation of the arc. License: the descriptive aggregate-hider (D lossy at fixed D) is UNAFFECTED (a geometric fact, no returns); the result does NOT license "incremental return information beyond the characteristics" or "a new return factor." The paper retreats to the descriptive decomposition + measurement object; the return section honestly states its predictability is not robustly distinct from the characteristics.

Nonlinear reducibility kill (final return-side test; pre-committed — PREREG_NONLIN.md, run_nonlin.py). The single unrun, most lethal residual: does C₁* survive beyond a NONLINEAR expansion of the ten reads (10 squares + all 45 pairwise products) as controls? Committed: RESURRECT = later-era t≥+2.0 AND coef≥0.5× baseline; DEAD = else. Result: DEAD (total). Later era (n99): C₁* coef=+0.000214, t=+0.62, ratio 0.24 — both criteria fail. Pre-2016 (n26, UNBANKABLE): t=+3.07 survives, but n=26 and NOT pursued per the spec (chasing it is the motivated save). Committed verdict: the return contribution is reducible to the reads even nonlinearly. THE RETURN QUESTION IS CLOSED. License: closes the return contribution; does not license a factor, a general effect, or a mechanism; the descriptive aggregate-hider was out of scope and is unaffected. Manuscript reducible linearly AND nonlinearly; re-frozen. STOP — no further return-side tests.

14. Provenance

Data: data_cache/*.parquet (Yahoo ETFs; Sharadar survivorship-free bulk). Gates: LOCKED_CRITERION.md, PRE-REGISTRATION_v2/v3/pathB/pathC.md (unedited post-run). Runners: run_horserace_v2/v3.py, run_pathB/C_sharadar.py, factor-zoo, robustness. Confirmation + audits (2026-08): run_confirmation.py (frozen harness), verify_characterize.py, audit_confirmation.py, reconcile_D.py, geometry_compare.py, shape_descriptive.py, dominant_read_audit.py. Shape consequence + temporal (frozen, hashed): PREREG_SHAPE.md (9cd845b7…) / run_shape_consequence.py (381f9497…); PREREG_SHAPE_TEMPORAL.md (43da5237…) / run_shape_temporal.py; magnitude sort PREREG_PORTFOLIO.md (0280ab8f…) / run_portfolio.py. Referee-response + adversarial (2026-08): run_plain_joint.py, run_referee_response.py, adversary_check.py. Paper: RESEARCH_NOTE.md, MANUSCRIPT.md/.html, figures fig1-3. Result dumps *_RESULT.txt. Log: RESULTS_AND_LEARNINGS.md. This page: build_labbook.py.