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Appendix B: Provenance Index

A section of The Cosmic Recursion by Mayone Maha Rajan.

PROVENANCE INDEX

Every chapter ends with a boxed list of what it asserted and at what strength. This appendix collects those lists into one place and reorganises them by tag, so that the book's claims can be audited without reading the book.

It is also, unavoidably, a compression of the manuscript — and so it follows the same policy the manuscript recommends. The contested and analogical claims are reproduced in full below, because those are the ones a reader needs the exact wording of in order to attack. The established claims are not reproduced; they are counted, and they are in the chapters where they were made, with their derivations attached.

That asymmetry is deliberate. An index that reprints the safe claims and summarises the risky ones is the Golden Record policy of Chapter Ten, and it is the wrong way round.

B.1 What the tags mean

`[VERIFIED]` — Measured, replicated, and not seriously in dispute within the relevant field. If one of these is wrong, something has gone wrong in physics, not in this book.

`[SOURCED]` — Well-supported and standard, resting on a specific body of work, but either model-dependent, indirectly established, or subject to ongoing refinement. Reliable to build on; not immune to revision.

`[BOUNDARY]` — Genuinely contested, unresolved, or resting on assumptions competent people disagree about. Every one of these is a place where the book could be wrong without anyone having been careless.

`[ILLUSTRATIVE]` — A mapping from physics to human experience. Rhetorical, not evidential. Carries no weight whatsoever and is never used to support a physical claim.

A single claim may carry two tags where part of it is established and part is not. Those appear in both counts.

B.2 Distribution

| Chapter | Claims | VERIFIED | SOURCED | BOUNDARY | ILLUSTRATIVE | |---|---|---|---|---|---| | One | 10 | 5 | 3 | 2 | 1 | | Two | 13 | 8 | 4 | 2 | 1 | | Three | 13 | 8 | 6 | 3 | 2 | | Four | 14 | 10 | 4 | 4 | 1 | | Five | 16 | 9 | 7 | 5 | 1 | | Six | 15 | 13 | 2 | 7 | 0 | | Seven | 16 | 10 | 5 | 6 | 1 | | Eight | 15 | 12 | 1 | 5 | 1 | | Nine | 13 | 9 | 4 | 3 | 2 | | Ten | 16 | 11 | 6 | 4 | 1 | | Eleven | 14 | 4 | 5 | 6 | 2 | | Total | 155 | 99 | 47 | 47 | 13 |

Three observations about the shape of that table, since a reader is entitled to draw conclusions from it.

Chapter Eleven has the lowest proportion of verified claims in the book — four out of fourteen — and this is appropriate rather than embarrassing. It is the chapter about the far future, and the far future is not measured. A chapter on the end of the universe with a Chapter Six verification profile would be a chapter that was lying.

Chapters Six and Seven carry the highest contested counts. Chapter Six discusses objects whose radio emission mechanism has been unsolved for sixty years and a gravitational-wave background reported below the conventional detection threshold. Chapter Seven rests on the black hole information paradox, which is not resolved. Both chapters say so repeatedly in the main text.

Anyone using this book as a source should treat the `[VERIFIED]` column as usable and the `[BOUNDARY]` column as a reading list of open questions rather than as findings.

B.3 Every contested claim in the book

Grouped by chapter. These are the lines a hostile reader should attack first, and the ones most likely to need revision at the next printing.

Chapter One

  • Inflation is a strongly supported framework that would additionally erase the universe's initial conditions. Its generic predictions have held; its distinctive gravitational-wave signature has not been detected, and its falsifiability is contested within the field. (also SOURCED)
  • Proposed mechanisms include hippocampal neurogenesis, absence of linguistic scaffolding, and immature self-concept. No mechanism is established.

Chapter Two

  • Whether Landauer's principle constitutes a complete and non-circular exorcism of Maxwell's demon is disputed in the philosophy of physics literature. The experimental results are not disputed.
  • Forgetting appears to involve active, regulated mechanisms rather than passive decay. Specific proposals — synaptic homeostasis, engram modification, glymphatic clearance during sleep — are supported to varying degrees and the last is directly contested by recent work. (also SOURCED)

Chapter Three

  • The Jeans criterion identifies a mass threshold above which thermal pressure cannot resist gravitational collapse. It is a first approximation; real star formation is regulated by supersonic turbulence and magnetic fields. (also SOURCED)
  • Collapse proceeds by hierarchical fragmentation as the Jeans mass falls with rising density, terminating at the opacity limit around ~0.01 solar masses. (also SOURCED)
  • Deuterium fusion begins around 13 Jupiter masses (composition-dependent); sustained hydrogen fusion begins around 0.075 solar masses (~75–80 Jupiter masses). (also VERIFIED)

Chapter Four

  • Proton–proton fusion is rate-limited by the weak-interaction conversion of a proton to a neutron during a tunnelling encounter; the mean waiting time per proton in the solar core is of order a billion years. (also VERIFIED)
  • Core gamma photons undergo a random walk to the surface over an estimated 10⁴–10⁶ years, emerging as roughly twenty times as many optical photons; energy is conserved and entropy increases by a comparable factor. (also SOURCED)
  • Main-sequence luminosity scales approximately as M^3.5, and lifetime approximately as M^−2.5. (also VERIFIED)
  • Solar luminosity has risen ~30% over the Sun's lifetime; the faint young Sun paradox is not fully resolved.

Chapter Five

  • The leading revival mechanism is delayed neutrino heating aided by hydrodynamic instabilities. It remains difficult to reproduce robustly in 3D simulation. (also SOURCED)
  • Whether neutron star mergers are the dominant r-process site is unresolved; enrichment in old metal-poor stars suggests at least one faster channel, with magnetorotational supernovae and collapsars as candidates.
  • Presolar grains in primitive meteorites carry isotopic signatures identifying their parent stellar sources; some have inferred ages exceeding five billion years. (also VERIFIED)
  • Direct collapse to a black hole without a successful explosion is theoretically expected for a fraction of massive stars. The leading observational candidate, N6946-BH1, has been challenged by later infrared observations. (also SOURCED)
  • Post-traumatic growth research relies predominantly on retrospective self-reported change, which corresponds weakly with measured change in prospective designs; the general claim that adversity produces growth is not supported at the strength commonly asserted. Resilience — return to baseline — is the modal outcome of trauma exposure. (also SOURCED)

Chapter Six

  • Neutron stars have radii of ~10–12 km and masses typically ~1.4 solar masses; support comes from neutron degeneracy pressure plus short-range nuclear repulsion. The maximum mass is equation-of-state dependent and unsettled. (also VERIFIED)
  • Pulsar radio emission results from beamed radiation along a magnetic axis misaligned with the rotation axis. The coherent emission mechanism remains unsolved after nearly six decades. (also VERIFIED)
  • Pulsar glitches — abrupt spin-ups followed by relaxation — are attributed to angular momentum transfer from a decoupled interior superfluid via vortex unpinning, and constitute the principal observational window into neutron star interiors. (also SOURCED)
  • In June 2023, NANOGrav and three other pulsar timing array collaborations reported evidence for a nanohertz gravitational wave background via the Hellings–Downs angular correlation, at roughly 3–4σ. Likely source: a population of supermassive black hole binaries. (also VERIFIED)
  • The Pioneer plaque encodes solar position and launch epoch using the periods of fourteen pulsars referenced to the hydrogen hyperfine frequency. Its decodability by an unfamiliar recipient is disputed. (also VERIFIED)
  • FRB 200428, from the Galactic magnetar SGR 1935+2154, established magnetars as at least one FRB source. The full FRB population's origins remain unresolved. (also VERIFIED)
  • Neural oscillations and cross-frequency coupling are robustly observed and correlate with cognitive states. Binding-by-synchrony remains a contested hypothesis, and no claim is made here that psychiatric conditions are dysrhythmias. (also SOURCED)

Chapter Seven

  • EHT images of M87\ (2019) and Sgr A\ (2022) show the photon-ring shadow, roughly 2.5× the Schwarzschild diameter, not the horizon. Independent reanalyses have questioned aspects of the Sgr A\ image reconstruction. (also VERIFIED)*
  • The virtual-pair-at-the-horizon account of Hawking radiation is a heuristic widely regarded as misleading; the derivation concerns mode mixing between asymptotic regions. (also VERIFIED)
  • Hawking radiation has never been astrophysically observed. Laboratory analogue experiments test kinematics, not gravitational physics, and are contested.
  • These results indicate information preservation but do not supply a mechanism, are largely derived in simplified or AdS settings, and their interpretation is actively debated. The paradox is not resolved.
  • AdS/CFT is an exact duality in anti-de Sitter space. Our universe is not anti-de Sitter, and a holographic description of de Sitter cosmology remains open. (also SOURCED)
  • Memory for highly stressful events shows altered organisation and cue-dependent retrieval. The stronger claim of a distinct storage mechanism is contested. No clinical claim is made anywhere in this chapter. (also SOURCED, ILLUSTRATIVE)

Chapter Eight

  • In the Bullet Cluster (Clowe et al., 2006), lensing-derived mass tracks the collisionless galaxies rather than the X-ray gas that dominates the baryonic mass. Its collision velocity has been argued to be in tension with standard cosmology. (also VERIFIED)
  • Decades of direct detection experiments have produced no confirmed signal; much of the natural WIMP parameter space is excluded, and coherent neutrino scattering backgrounds were observed by LZ and XENONnT in 2024. (also VERIFIED)
  • The DAMA/LIBRA annual modulation claim remains unreplicated and is disfavoured by COSINE-100 and ANAIS.
  • MOND predicts the baryonic Tully–Fisher relation and the tight radial acceleration relation from baryonic distribution alone, which ΛCDM must reproduce through feedback. MOND fails on cluster dynamics, the Bullet Cluster, CMB peaks, and structure formation, and TeVeS was heavily constrained by GW170817. (also VERIFIED)
  • Small-scale challenges to cold dark matter (core-cusp, satellite populations) are substantially but not entirely addressed by baryonic physics.

Chapter Nine

  • A 2026 reanalysis applying systematics corrections to Gaia proper motions raised the probability substantially. Recent; status should be verified. (also SOURCED)
  • The M–σ relation links black hole mass to bulge velocity dispersion with low scatter. Its interpretation as evidence of feedback-driven co-evolution is contested; hierarchical merging plus central-limit averaging may account for much of it. (also VERIFIED)
  • Incentive-sensitization theory distinguishes dissociable "wanting" and "liking" systems, with the former sensitising under repeated exposure while the latter does not. The model is influential and contested, and no clinical claim is made here. (also SOURCED, ILLUSTRATIVE)

Chapter Ten

  • The 2012 "diamond planet" interpretation of 55 Cancri e rested on a host-star C/O ratio above 1, which was substantially revised downward in 2013. The claim continues to circulate. (also SOURCED)
  • Shankman et al. (2017) and Napier et al. (2021), using surveys with characterised biases, found the clustering consistent with observational selection effects at low significance. Batygin and Brown contest these analyses. The dispute turns on bias modelling. (also VERIFIED)
  • Alternative explanations include the collective self-gravity of a massive primordial scattered disk. Cassini ranging and infrared all-sky surveys constrain but do not exclude the hypothesis. (also SOURCED)
  • That figure is conditional on Planet Nine's existence with approximately the proposed parameters. The unconditional probability is lower and is not reliably quantifiable given current disagreement over the clustering evidence.

Chapter Eleven

  • DESI baryon acoustic oscillation data, combined with CMB and supernova datasets, have shown a preference for evolving dark energy at roughly 3–4σ. The significance depends materially on which supernova compilation is used, and the question is actively contested. Readers should check its current status. (also VERIFIED)
  • Proton decay is predicted by many grand unified theories and has never been observed; Super-Kamiokande limits exceed 10³⁴ years. (also VERIFIED)
  • Poincaré recurrence applies to a finite-entropy de Sitter universe on timescales of order 10^(10¹²²) years. The associated Boltzmann brain problem is generally treated as a constraint disfavouring models, not as a positive prediction. (also SOURCED)
  • Penrose's Conformal Cyclic Cosmology is a minority proposal requiring the eventual disappearance of all rest mass and black hole information loss; its claimed CMB signatures have not been independently confirmed.
  • The Everett interpretation makes no distinguishing observational predictions and does not license claims about accessible alternative personal histories. (also ILLUSTRATIVE)
  • The Four-Slot schema's Operator was epistemic rather than physical in Chapters Eight and Ten. This is a genuine strain on the framework, flagged in both chapters and acknowledged here, and constitutes the strongest available objection to the book.

B.4 Every analogical claim in the book

Each of these is a mapping from physics to human experience. None of them is evidence. If every line below were deleted, no physical claim in the book would be affected.

Chapter One

  • The mapping between cosmic and developmental forgetting is analogical. Both systems discard instances and retain parameters under a shared constraint — large input, bounded retention, irreversible transition — and there is no claimed shared mechanism.

Chapter Two

  • The mapping from thermodynamic erasure cost to attentional and mnemonic economy is analogical. Shared constraint type — bounded capacity, mandatory selection, real cost — with no claimed shared mechanism.

Chapter Three

  • Creation myths involving the dismemberment of a primordial body describe total conversion of the precursor into the world. This is structurally analogous to star formation and quantitatively wrong about it.
  • The mapping from ignition thresholds to human endeavour is analogical and asserts only that discontinuous thresholds exist and are condition-dependent. No claim is made that human capacity is fixed at formation.

Chapter Four

  • All mappings from stellar stability to human practice are analogical. The transferable claims are that output and duration trade superlinearly, and that stability requires a structural feedback channel rather than intent.

Chapter Five

  • The phoenix myth asserts continuity of identity through catastrophe. Nucleosynthesis asserts continuity of material through the destruction of identity. These are structurally different claims.

Chapter Seven

  • Memory for highly stressful events shows altered organisation and cue-dependent retrieval. The stronger claim of a distinct storage mechanism is contested. No clinical claim is made anywhere in this chapter. (also SOURCED, BOUNDARY)

Chapter Eight

  • The mapping from measurement-channel invisibility to institutional invisibility is analogical, and asserts only that absence from a record may reflect the instrument's coupling rather than the subject's significance.

Chapter Nine

  • Incentive-sensitization theory distinguishes dissociable "wanting" and "liking" systems, with the former sensitising under repeated exposure while the latter does not. The model is influential and contested, and no clinical claim is made here. (also SOURCED, BOUNDARY)
  • The wendigo is drawn from living Algonquian traditions and is not used here as a generic symbol of greed.

Chapter Ten

  • The Voyager Golden Record's contents were curated toward favourable material, producing a systematically biased representation with no internal indication of the bias. Its pulsar-map cover is fully auditable. (also VERIFIED)

Chapter Eleven

  • The Everett interpretation makes no distinguishing observational predictions and does not license claims about accessible alternative personal histories. (also BOUNDARY)
  • In Norse eschatology the gods do not return; a remnant survives and the game pieces of the old order are found in the new grass. Of the cyclical traditions surveyed, this is the one whose structure matches the physics.

B.5 Two claims that carry no tag

Two lines in the claims boxes are untagged, and both are deliberate.

Chapter Ten — "The author's Planet Nine detection-probability forecast was corrected from 61.3% to 71.9% cumulative by 2036 after identifying an incorrect declination cutoff in the survey coverage model." This is marked `[VERIFIED — author's own work]`, which is not one of the four registers. It is a claim about something I did rather than about the world, and its verification route is different from all the others: not the literature, but a published record with prior revisions retained and a code path that can be inspected. Readers should weigh it accordingly, and with the awareness that I am the interested party.

Chapter Eleven — "Across eleven chapters, no examined system retained its input rather than a compressed invariant." This is a claim about the book, not about physics. It cannot be tagged on the same scale because its evidence is the manuscript itself.

B.6 What would have to change

If the following turned out otherwise, the sections resting on them would need rewriting rather than adjusting.

  • Landauer's principle, if the philosophical circularity objection (Norton, Earman) were established rather than merely argued. Chapter Two's keystone, and therefore the book's floor.
  • The Bekenstein bound's generality, if the entropy-area relation proved specific to black holes rather than universal. Chapter Seven, and therefore the book's ceiling.
  • Dark matter, if a modified-gravity account succeeded at cluster and cosmological scales. Chapter Eight substantially; Chapter Ten's Neptune-versus-Vulcan argument gains rather than loses.
  • Planet Nine, either way. Chapter Ten is built to survive both outcomes, and says so.
  • Evolving dark energy, if the DESI preference strengthens. Chapter Eleven's far-future picture changes materially; the erasure argument survives in modified form.
  • Post-traumatic growth, if prospective designs began reliably confirming self-reported change. Chapter Five's refusal would need softening, and I would rather find that out than not.

Six items. If none of them moves in the next decade, this book has held. If several move, the compression thesis may still stand while a good deal of its scaffolding does not.