# Sundog v Riemann Ledger

> **Cross-substrate failure-map entry:** VACUOUS (Path i — the `Z2`-descent
> rigidity check is trivially satisfied on gap-only features) — see
> [`CROSS_SUBSTRATE_NOTES.md`](CROSS_SUBSTRATE_NOTES.md)
> "Cross-Substrate Generality Failure Map".

Working hook:

> A shadow might have less information than the body, but sometimes it is more
> rigid, more testable, and more useful.
>
> Publish the projection. Publish where it breaks. The failure boundary is the
> credential.

This ledger stages a narrow, apparatus-coupling investigation between Sundog's
traceable-projection and choreographic toolkit and selected structures around
the Riemann Hypothesis (RH). It treats RH-adjacent objects - zero statistics,
explicit formulae, periodic-orbit analogies, and candidate spectral
realizations - as targets for bounded, pre-registered stress-testing and
projection work using the repo's existing geometry, symmetry, and falsification
machinery.

This is not a claim to RH progress. It is a claim that Sundog has a disciplined
way to produce receipts against public mathematical targets, including null and
falsifying receipts.

Status: drafting. Lit-pass and bridge scoping landed 2026-05-28; see
[`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md) and
[`riemann/REPRESENTATION_BRIDGE_NOTES.md`](riemann/REPRESENTATION_BRIDGE_NOTES.md).
Probe 01 v1 has one Path (i) parity-decomposition receipt filed at
[`riemann/receipts/2026-05-28_probe01_pathi_parity_decomposition.md`](riemann/receipts/2026-05-28_probe01_pathi_parity_decomposition.md).
The first Front-A reading note is drafted at
[`riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md`](riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md).
Its first cell-set companion is filed at
[`riemann/RIEMANN_C1_CELLSET_V0.md`](riemann/RIEMANN_C1_CELLSET_V0.md).
The C1 linearity audit opens a nonlinear zero-statistics scoping lane at
[`riemann/NONLINEAR_PAIR_CORRELATION_LANE.md`](riemann/NONLINEAR_PAIR_CORRELATION_LANE.md).
Its bridge note admits only the S2 gap-pair swap as a reversibility-test hook;
Probe 05 v0 is filed at
[`riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md`](riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md)
and was executed 2026-05-28, returning the pre-registered `R-NL-NEG-A`
reversibility null at
[`riemann/receipts/2026-05-28_probe05_reversibility_null.md`](riemann/receipts/2026-05-28_probe05_reversibility_null.md).
Three independent lanes (Path (i) Z2 / C1 explicit-formula / nonlinear S2) have
now each returned a clean documented null by a distinct identified cause; the
cross-lane reading is consolidated at
[`riemann/RIEMANN_BOUNDED_NULL_SYNTHESIS.md`](riemann/RIEMANN_BOUNDED_NULL_SYNTHESIS.md).
No structural-zero edge has been found, and the synthesis records why none is
expected in these substrates. External review is the registered gate before any
public-facing claim.

## Claim Boundary

This document explicitly does **not** claim:

- a proof of RH;
- a disproof of RH;
- a candidate Hilbert-Polya operator;
- a new formula for the zeros;
- universal or unbounded applicability of any projection.

What this ledger does stage:

- a defensible evaluator lens: application of the choreography catalog,
  isotropy v0.3 derivations, gauge cocycles, Procrustes alignment, and
  projection discipline as a stress-test and receipt-generation apparatus on
  existing, publicly verifiable RH-adjacent data and conjectures;
- a horizon coupling claim: exploration of whether choreographic invariants and
  traceable projections can yield narrow, falsifiable statements about
  periodic-orbit / trace-formula analogies in restricted computational or
  analytic windows;
- pre-registered falsifiers, named failure surfaces, and evidence tiers so any
  positive, null, or negative result remains traceable and auditable.

This is in the direct lineage of [`SUNDOG_V_CAPSET.md`](SUNDOG_V_CAPSET.md),
which couples the evaluator to hard external mathematics, and
[`SUNDOG_V_ISOTROPHY_KFACET.md`](SUNDOG_V_ISOTROPHY_KFACET.md) /
[`SUNDOG_V_THREEBODY.md`](SUNDOG_V_THREEBODY.md), which carry the
choreographic and dynamical machinery with explicit structural-zero and
boundary receipts.

## The Coupling Claim

The coupling is staged on two fronts.

### Front A - Evaluator / Stress-Test Lens

Sundog's existing tools can be applied as a lens to:

- pair correlations, nearest-neighbor spacings, and higher statistics of
  computed Riemann zeros;
- terms or smoothed versions of the explicit formulae;
- candidate periodic-orbit models or abstract dynamical systems proposed in the
  literature as analogs for the zeros.

The initial apparatus set is:

- 21 strict single-curve G.2 choreographies;
- S3-action parity and induced-representation tracking;
- isotropy v0.3 twist operator, F_beta template, and tau-flag;
- gauge cocycles and Procrustes alignment;
- closure-relative residuals;
- photometric-style traceable projections;
- three-body dynamical stress-testing discipline.

Any alignment, mismatch, or structural-zero receipt generated is first-class
data. The claim is live only inside explicitly bounded domains such as a
pre-registered zero-height window, named statistics, and fixed smoothing
kernels.

### Front B - Choreographic / Projection Substrate

A narrower, more ambitious lane treats the explicit formula / Gutzwiller-style
trace relation as a Sundog-style traceable projection from classical periodic
data - primes or modeled choreographic orbits - onto a readable shadow on or
near the critical line.

Front B requires:

- an exact domain;
- named smoothing;
- fixed invariants;
- a declared projection map;
- a residual or variance threshold that falsifies the projection;
- no expansion after result inspection.

Front B remains horizon until Front A has generated initial receipts and the
falsification surface for the projection is locked.

## Falsification Surface

The coupling claim is falsified or bounded by any of the following named modes.
These take precedence over narrative success.

1. **Invariant mismatch after alignment** - Choreographic invariants such as
   `E`, `|L|`, or derived gauge-cocycle quantities show no statistically or
   structurally significant alignment, post-Procrustes / gauge cocycle, with
   zero statistics or explicit-formula terms inside the pre-registered window.
   Receipt: closure residual exceeds threshold, or catalog-asymmetric behavior
   appears under bare `(12)` or the induced-representation track.
2. **Isotropy v0.3 structural failure** - Application of the twist operator,
   induced-representation `d_i` formula, F_beta template, or tau-flag to
   zero-pair data, phases, or explicit terms yields widespread structural-zero
   receipts or quarantined representations inconsistent with the registered
   expectation, or produces no usable catalog.
3. **Projection residual breach** - Any proposed trace/projection from periodic
   data to smoothed zero counts or variance deviates beyond the registered
   residual or variance threshold in the chosen smoothing/window. Failure is
   declared at the first named surface crossed.
4. **Dynamical escape under stress-test** - Three-body or generalized n-body /
   abstract dynamical realizations of candidate orbit analogs produce
   out-of-bounds behavior, collapse, or mismatch with zero-derived statistics
   when run under the same guardrails used in `SUNDOG_V_THREEBODY.md`.
5. **Domain leakage / scope creep** - A claim live only inside a bounded domain
   requires expansion of that domain without new, independent receipts. This
   quarantines the claim to its original envelope.

Null result is valid data. A clean structural-zero receipt or consistent
failure to align inside the registered window counts as a durable outcome.

## Initial Domain Map

All claims are gated by explicit domains. Expansion requires a new phase sign-off
and updated falsifiers.

- **Zero height window**: first `N` zeros, generated or sourced by one named
  method, with the target envelope initially limited to imaginary part below
  about `1e4`.
- **Statistics**: nearest-neighbor spacings and pair correlations are primary.
  Higher n-point functions remain horizon.
- **Smoothing / explicit formula windows**: only named smoothing kernels and
  cutoff scales are admitted. Unsmoothed or arbitrarily large windows are out
  of scope.
- **Dynamical models**: abstract or low-dimensional choreographic analogs only.
  Full adelic or noncommutative-geometry realizations remain horizon.
- **Symmetry actions**: S3 / induced-representation and O(3)-style parity
  analysis on pair data or orbit catalogs. Full Galois or class-field actions
  are out of scope.

Failure map summary:

- inside domain plus alignment within residual -> bounded positive receipt;
- inside domain plus structural zero or residual breach -> falsified in that
  cell; claim downgraded or quarantined;
- outside domain -> no claim; apparent signal is exploratory only.

## Sundog Expression

| Sundog tool | RH / zeta target | Expression / probe | Primary falsifier |
| --- | --- | --- | --- |
| 21 strict G.2 choreographies + S3 parity + induced-rep track | Periodic-orbit analogs, length spectra | Align invariants (`E`, `|L|`) via Procrustes + gauge cocycles; check catalog asymmetry | 1, 2 |
| Isotropy v0.3: twist, F_beta, tau-flag, structural zero | Zero pair spacings, phases, explicit terms | Run induced-rep `d_i` and F_beta template; catalog quarantined cases | 2 |
| Gauge cocycles + Procrustes | Spectral alignment / trace matching | Measure closure residuals post-alignment | 1, 3 |
| Three-body / dynamical stress | Candidate orbit dynamics | Guarded TRACK control; observe escapes versus zero-derived statistics | 4 |
| Photometric / traceable projections | Explicit formula as trace/projection | Define smoothing window + readable shadow; register residual threshold | 3 |
| Coarse-graining / signature sufficiency | Prime-zero relations via invariants | Test whether choreographic signatures act as sufficient statistics for smoothed counts | 1, 3 |

## Initial Probe Shortlist

Each probe must produce a dated receipt note before escalation. Positive, null,
and falsifying receipts all count.

### Probe 1 - Isotropy v0.3 on Low-Lying Zero Pair Data

- **Attacks failure mode(s):** 2 (isotropy v0.3 structural failure), 5 (domain leakage).
- **Cost:** Low.
- **Front:** A (evaluator / stress-test lens).
- **Admitted bridge:** Path (i) Z₂-descent under
  [`riemann/REPRESENTATION_BRIDGE_NOTES.md`](riemann/REPRESENTATION_BRIDGE_NOTES.md);
  Path (ii) S₃-via-triple deferred to a future Probe 01b.
- **Lit-pass disposition:** conditionally admitted; see
  [`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md) Track A. Structural-zero
  discipline does not carry across the Z₂-descent; expected receipt category is
  null receipt or catalog-asymmetry under `(12)`, not v0.3h-strength structural-zero.
- **External review path:** an analytic number theorist familiar with pair-correlation
  and unfolded-spacing statistics (Goldston / Suriajaya / Turnage-Butterbaugh tradition).
  Named at promotion.
- **First receipt:** 2026-05-28 Path (i) run on the first 5,000 Odlyzko
  `zeros1` ordinates produced a bounded Front A parity-decomposition receipt;
  spacing-derived features were reflection-even under the registered mirrored
  pair construction. This is not a structural-zero receipt and does not test RH.
  See
  [`riemann/receipts/2026-05-28_probe01_pathi_parity_decomposition.md`](riemann/receipts/2026-05-28_probe01_pathi_parity_decomposition.md).

Apply the v0.3 pipeline - twist operator, induced-representation cases, F_beta
template, and tau-flag - to nearest-neighbor spacings and pair correlations of
the first registered zero window, restricted to the Z₂-descent sector per the
bridge notes.

Receipt fields:

- zero source and source hash or generator version;
- `N`, maximum height, and unfolding method;
- structural-zero count;
- quarantined representations;
- catalog asymmetry under registered actions;
- failure-mode disposition.

Pre-registration scaffold:
[`docs/prereg/riemann/P0_DOMAIN_AND_RECEIPT_LOCK.md`](prereg/riemann/P0_DOMAIN_AND_RECEIPT_LOCK.md).

Probe spec:
[`docs/riemann/PROBE_01_ISOTROPY_ZERO_PAIRS_SPEC.md`](riemann/PROBE_01_ISOTROPY_ZERO_PAIRS_SPEC.md).

### Probe 2 - Choreography Invariant Alignment to Explicit Formula Terms

- **Attacks failure mode(s):** 1 (invariant mismatch after alignment), 3 (projection residual breach).
- **Cost:** High.
- **Front:** A leaning B (substrate alignment).
- **Lit-pass disposition:** **deferred / likely voided.** See
  [`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md) probe-ranking table.
  Choreography invariants (`E`, `|L|`) and explicit-formula terms live in
  different physical / algebraic categories with no published coupling; risk
  of producing a Front-A miscalibration receipt is high. Hold until Probe 01
  + bridge notes land and reconsider whether to void or replace with a
  cleaner Front-A reading note. First replacement draft filed at
  [`riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md`](riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md).
- **External review path:** would require both an n-body dynamicist (Simó /
  Moeckel / Chenciner tradition) and an analytic number theorist; cross-domain
  review is itself a cost flag.

Take a small, registered set of strict single-curve choreographies. Compute
invariants. Align via Procrustes + gauge cocycle against smoothed
explicit-formula contributions in a narrow, named window.

Receipt fields:

- choreography row set;
- invariant vector definition;
- smoothing kernel and cutoff;
- alignment map;
- closure residual;
- mismatch or structural-zero disposition.

### Probe 3 - Projection Residual Test: Smoothed Trace

- **Attacks failure mode(s):** 3 (projection residual breach), 5 (domain leakage).
- **Cost:** Low-Med.
- **Front:** B (choreographic / projection substrate) — narrow pilot.
- **Lit-pass disposition:** admissible if **re-scoped to operational discipline,
  not a new projection.** Smoothed explicit-formula machinery (Riemann, Weil,
  Burnol, smoothed Landau) is mature; Connes' adèle-class-space program already
  reads the explicit formula as a trace formula in noncommutative geometry.
  Sundog's edge here is pre-registered residual threshold + publish-the-falsifier
  discipline, not a new projection. See
  [`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md) Track B + Connes
  competitor note.
- **Staged cell set (pending review):** a candidate explicit-formula cell set
  for this probe is filed in
  [`riemann/RIEMANN_C1_CELLSET_V0.md`](riemann/RIEMANN_C1_CELLSET_V0.md),
  following the scaffold in
  [`riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md`](riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md).
  It is **not adopted** until the Front-A reading clears its external sanity
  check; the note's
  `R-C1-NEG-A`/`R-C1-NEG-B` (vacuity / identity-zero laundering) negatives gate
  whether Probe 03 has any edge beyond standard even-test-function bookkeeping.
- **External review path:** an analytic number theorist comfortable with
  smoothed explicit formulae (Iwaniec–Kowalski idiom). Named at promotion.

Define one concrete smoothing/window on the explicit formula. Treat periodic
data - primes or choreographic orbit lengths - as source. Publish the exact
projection map and numerical residual/variance threshold that constitutes
falsification. Run and record outcome.

Receipt fields:

- source periodic data;
- smoothing kernel;
- projection operator;
- residual threshold;
- observed residual / variance;
- first crossed falsifier, if any.

### Probe 4 - Three-Body Stress on Abstract Orbit Analog

- **Attacks failure mode(s):** 4 (dynamical escape under stress-test), 5 (domain leakage).
- **Cost:** Med.
- **Front:** B (dynamical substrate).
- **Lit-pass disposition:** **downgraded.** The quantum-chaos / periodic-orbit
  literature for trace formulae is very deep (Berry–Keating, Bogomolny,
  Cvitanović school) and likely overshadows a three-body-stress version.
  Note the numerical 21-vs-21 coincidence — the v0.3h strict G.2 catalog has
  21 choreographies and Li–Liao 2025 ([2508.08568](https://arxiv.org/abs/2508.08568))
  reported 21 3D choreographic periodic orbits for equal masses; *no substrate
  claim follows from this coincidence.* It is a re-audit hook, not evidence.
  Defer until Probe 01 lands.
- **External review path:** a periodic-orbit-theory researcher in the
  Cvitanović / Sieber–Richter tradition. Named at promotion.

Instantiate a minimal dynamical analog inspired by periodic-orbit thinking
inside a guarded three-body-style workbench. Apply the same TRACK / boundary
discipline used in `SUNDOG_V_THREEBODY.md`. Observe whether zero-derived
statistics act as a stabilizing or destabilizing signal.

Receipt fields:

- analog definition;
- controller mode;
- guard thresholds;
- zero-derived signal construction;
- escape/collapse/mismatch events;
- operating-envelope disposition.

### Probe 5 - Nonlinear Gap-Pair Reversibility Test

- **Attacks failure mode(s):** nonlinear-lane `R-NL-NEG-A` (GUE dominance),
  `R-NL-NEG-B` (representation triviality), `R-NL-NEG-C` (sampling-floor
  failure), and main-ledger Mode 5 (domain leakage).
- **Cost:** Low.
- **Front:** A (zero-statistics evaluator / stress-test lens).
- **Bridge disposition:** admitted only on the S2 consecutive-gap-pair swap,
  per
  [`riemann/NONLINEAR_PAIR_CORRELATION_BRIDGE_NOTES.md`](riemann/NONLINEAR_PAIR_CORRELATION_BRIDGE_NOTES.md).
  C3 triples are quarantined as relabeling; residual sign-bins are downgraded
  to ordinary GUE residual analysis.
- **Expected outcome:** bounded null / `R-NL-NEG-A`. The statistic is
  non-forced per sample, but the sine-kernel / GUE baseline predicts
  reversibility, hence `E[D] = 0`.
- **Probe spec:** filed at
  [`riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md`](riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md).
- **External review path:** an analytic number theorist or random-matrix /
  point-process reviewer familiar with Montgomery-Odlyzko statistics and
  consecutive-gap tests.

Test the arrow-of-time statistic
`D = (# {s_i > s_{i+1}} - # {s_i < s_{i+1}}) / (N_zero - 2)` on registered
consecutive unfolded gaps. A clean null is useful as a documented boundary: the
apparatus has no structural-zero edge here because GUE already predicts the
null. A non-null result is treated only as a finite-window reversibility anomaly
requiring independent replication.

Receipt fields:

- zero source, `N_zero`, height, and unfolding rule;
- gap-pair construction;
- tie tolerance;
- `D`, orientation counts, and tie count;
- analytic and block-bootstrap floors;
- named nonlinear-lane disposition.

## Promotion Criteria

This ledger graduates to a phased `SUNDOG_V_RIEMANN_ROADMAP.md` only when all
of the following are met:

1. at least two initial probes have produced durable, auditable receipts;
2. the falsification surface has been exercised at least once with a named
   failure mode triggered or cleanly avoided;
3. a bounded Front A claim can be stated with registered domains and falsifiers
   and survives internal audit;
4. Front B has a concrete, narrow pilot specification that does not rely on
   scope creep.

Until then, this remains a ledger for disciplined coupling and receipt
generation.

## Horizon

Explicitly not claimed:

- a Sundog-flavored dynamical realization whose spectrum or trace reproduces
  low-lying zero statistics inside a registered envelope;
- coarse-graining postulates applied to prime-zero relations;
- linkage to mesa-style subspace localization or 5D entanglement analogies in
  spectral data;
- contribution to Millennium Prize-level attack surface beyond falsifiable
  infrastructure.

These remain horizon until receipts exist.

## Project Files

- [`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md) - 2026-05-28 lit-pass
  anchoring the probe ranking; gap claims time-stamped.
- [`docs/riemann/README.md`](riemann/README.md) - project index and artifact
  map.
- [`docs/riemann/RIEMANN_BOUNDED_NULL_SYNTHESIS.md`](riemann/RIEMANN_BOUNDED_NULL_SYNTHESIS.md)
  - capstone bounded-null synthesis: three lanes, three identified causes, no
  structural-zero edge; public surface gated on external review.
- [`docs/riemann/EXTERNAL_REVIEW_PACKET.md`](riemann/EXTERNAL_REVIEW_PACKET.md)
  - minimal external-review packet and three-question sanity-check ask.
- [`docs/riemann/EXTERNAL_REVIEW_EMAIL_DRAFT.md`](riemann/EXTERNAL_REVIEW_EMAIL_DRAFT.md)
  - email drafts for requesting review without implying endorsement.
- [`docs/riemann/REPRESENTATION_BRIDGE_NOTES.md`](riemann/REPRESENTATION_BRIDGE_NOTES.md)
  - bridge scoping resolving the v0.3h-D3 vs Riemann-Z₂ admissibility question
  for Probe 01.
- [`docs/riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md`](riemann/FRONT_A_FUNCTIONAL_EQUATION_READING.md)
  - draft Front-A reading note: functional-equation reflection as a receipt
  scaffold for smoothed explicit formulae.
- [`docs/riemann/RIEMANN_C1_CELLSET_V0.md`](riemann/RIEMANN_C1_CELLSET_V0.md)
  - v0 explicit-formula parity scaffold for the Front-A reading; unreviewed and
  unrun.
- [`docs/riemann/NONLINEAR_PAIR_CORRELATION_LANE.md`](riemann/NONLINEAR_PAIR_CORRELATION_LANE.md)
  - scoping note for a nonlinear pair-correlation / gap-statistics lane opened
  by the C1 linearity audit.
- [`docs/riemann/NONLINEAR_PAIR_CORRELATION_BRIDGE_NOTES.md`](riemann/NONLINEAR_PAIR_CORRELATION_BRIDGE_NOTES.md)
  - bridge scoping for the nonlinear lane; admits only the S2 gap-pair
  reversibility hook and pre-registers NEG-A as expected.
- [`docs/prereg/riemann/P0_DOMAIN_AND_RECEIPT_LOCK.md`](prereg/riemann/P0_DOMAIN_AND_RECEIPT_LOCK.md)
  - initial domain and admission lock.
- [`docs/riemann/PROBE_01_ISOTROPY_ZERO_PAIRS_SPEC.md`](riemann/PROBE_01_ISOTROPY_ZERO_PAIRS_SPEC.md)
  - first executable probe specification; Path (i) v1 run filed, while Path
  (ii) remains deferred.
- [`docs/riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md`](riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md)
  - v0 nonlinear zero-statistics reversibility-test spec; S2 hook only,
  expected disposition `R-NL-NEG-A`.
- [`docs/riemann/RECEIPT_TEMPLATE.md`](riemann/RECEIPT_TEMPLATE.md) - receipt
  template for every probe result.
- [`docs/riemann/receipts/2026-05-28_probe01_pathi_parity_decomposition.md`](riemann/receipts/2026-05-28_probe01_pathi_parity_decomposition.md)
  - first dated Probe 01 v1 receipt under Path (i).
- [`docs/riemann/receipts/2026-05-28_probe05_reversibility_null.md`](riemann/receipts/2026-05-28_probe05_reversibility_null.md)
  - dated Probe 05 S2 reversibility null; `R-NL-NEG-A` as predicted.
- [`experiments/riemann/README.md`](../experiments/riemann/README.md) -
  computational workspace notes.

## Cross-References

- [`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md) - 2026-05-28 lit-pass
  memo grounding the probe ranking in indexed prior art.
- [`riemann/RIEMANN_BOUNDED_NULL_SYNTHESIS.md`](riemann/RIEMANN_BOUNDED_NULL_SYNTHESIS.md)
  - capstone bounded-null synthesis and current conclusion of the Front-A
  Riemann lane.
- [`riemann/REPRESENTATION_BRIDGE_NOTES.md`](riemann/REPRESENTATION_BRIDGE_NOTES.md)
  - bridge scoping for Probe 01 admissibility.
- [`riemann/NONLINEAR_PAIR_CORRELATION_BRIDGE_NOTES.md`](riemann/NONLINEAR_PAIR_CORRELATION_BRIDGE_NOTES.md)
  - nonlinear bridge scoping for Probe 05; S2 admitted, C3 quarantined,
  residual bins downgraded.
- [`riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md`](riemann/PROBE_05_NONLINEAR_ZERO_STATISTICS_SPEC.md)
  - v0 reversibility-test spec for consecutive unfolded gaps.
- [`SUNDOG_V_NAVIERSTOKES.md`](SUNDOG_V_NAVIERSTOKES.md) - kin ledger filed
  same day (2026-05-28); same capset-pattern structure with lit-pass + C1
  reading note + cell-set v0 + fiber protocol artifacts.
- [`SUNDOG_V_ISOTROPHY_KFACET.md`](SUNDOG_V_ISOTROPHY_KFACET.md) - compatibility
  pointer to the canonical isotrophy ledger.
- [`docs/isotrophy/SUNDOG_V_ISOTROPHY_KFACET.md`](isotrophy/SUNDOG_V_ISOTROPHY_KFACET.md)
  - v0.3 derivations, structural-zero catalog, induced-rep track, and F_beta
  template. **Load-bearing for the bridge question** — v0.3h is built on the
  D3 representation; the bridge notes resolve the descent to Riemann's
  natural Z₂ reflection symmetry.
- [`SUNDOG_V_THREEBODY.md`](SUNDOG_V_THREEBODY.md) - guarded dynamical
  stress-testing, TRACK control, failure boundaries.
- [`SUNDOG_V_CAPSET.md`](SUNDOG_V_CAPSET.md) - precedent for coupling Sundog's
  apparatus to external hard mathematics.
- [`SUNDOG_V_MESA.md`](SUNDOG_V_MESA.md) - mesa cliff, subspace localization,
  and operating-envelope style.
- [`SCIENTIFIC_CRITERIA.md`](SCIENTIFIC_CRITERIA.md) - testable versus
  non-testable distinctions.
- [`COARSE_GRAINING_PROOF_ROADMAP.md`](COARSE_GRAINING_PROOF_ROADMAP.md) -
  related postulates on signatures and sufficiency.

## Inspection Trail

Consolidated and dated in [`RIEMANN_LITPASS_MEMO.md`](RIEMANN_LITPASS_MEMO.md)
(2026-05-28). The targets below are reading anchors; the lit-pass memo gives
the indexed-prior-art status, gap claims, and per-probe disposition.

- Montgomery pair correlation conjecture and Odlyzko numerical evidence; the
  2024 unconditional Montgomery theorem and 2025 simple-zero / critical-line
  proportions (lit-pass Track A).
- Berry–Keating, Bogomolny, and the broader quantum-chaos / trace-formula
  reading (lit-pass Track B).
- Connes' adèle-class-space program and the 2024 Connes–Consani–Moscovici
  prolate-wave-operator integration (lit-pass Track B, dominant competitor).
- Explicit formulae in the Riemann and Weil traditions; smoothed Landau
  variants (lit-pass Track B, Probe 03 substrate).
- Hilbert–Pólya conjecture and 2024–2025 spectral-realization candidates
  (lit-pass Track C).
- Functional equation reflection symmetry `s -> 1 - s` as the canonical Z₂
  target; bridge resolved in
  [`riemann/REPRESENTATION_BRIDGE_NOTES.md`](riemann/REPRESENTATION_BRIDGE_NOTES.md).
- Public zero tables (Odlyzko `10^20` and `10^22` neighborhoods) for
  reproducible Probe 01 input.

External references are targets for the apparatus. No original mathematical
claim is imported or asserted by listing them here. Time-stamp re-audit
windows live in the lit-pass memo.