References

#Endnotes

1. History of the Fibonacci sequence in Indian prosody (Piṅgala, Virahāṅka, Gopāla, Hemachandra). See the historical summary in the Fibonacci sequence overview: https://en.wikipedia.org/wiki/Fibonacci_sequence and the On-Line Encyclopedia of Integer Sequences entry A000045: https://oeis.org/A000045. ↩
2. Leonardo of Pisa ("Fibonacci"), Liber Abaci (1202), and the rabbit-population problem as the sequence's European introduction. See: https://www.cut-the-knot.org/arithmetic/combinatorics/FibonacciTilings.shtml and https://en.wikipedia.org/wiki/Fibonacci_sequence. ↩
3. Internal Odisena canonical source (privacy-safe): the Helios 1 Worldbuilding redirect convention, in which renamed entries receive explicit redirect records and an architecture index so old titles remain discoverable. See Appendix I, item 8. ↩
4. The Fibonacci Q-matrix identity $(\begin{array}{cc}1& 1\\ 1& 0\end{array}{)}^n=(\begin{array}{cc}{F}_{n+1}& F_n\\ F_n& F_{n-1}\end{array})$. See: https://www.cut-the-knot.org/arithmetic/algebra/FibonacciMatrix.shtml and https://cp-algorithms.com/algebra/fibonacci-numbers.html. ↩
5. Internal Odisena canonical source (privacy-safe): the AVPT CI/CD snapshot-first deployment cadence — preserve pre-deployment state, validate, and track rollback/drift. See Appendix I, item 4. ↩
6. Convergence of consecutive Fibonacci ratios to the golden ratio $\phi =(1+\sqrt{5})/2$. See: https://oeis.org/A000045 and the standard derivation via $r=1+1/r$. ↩
7. Binet's formula $F_n=({\phi }^n-{\psi }^n)/\sqrt{5}$, and $F_n$ as the nearest integer to ${\phi }^n/\sqrt{5}$. See: https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html and https://cp-algorithms.com/algebra/fibonacci-numbers.html. ↩
8. Internal Odisena canonical source (privacy-safe): field-validation recovery treats each attempt as an empirical cycle that preserves partial state and logs evidence. See Appendix I, item 6. ↩
9. Cassini's identity $F_{n-1}{F}_{n+1}-F_n^2=(-1{)}^n$. See: https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities and https://mathworld.wolfram.com/CassinisIdentity.html. ↩
10. Phyllotaxis and the golden angle (~137.5°); Douady and Couder's magnetized-droplet experiments; efficient packing. See the phyllotaxis review: https://archive.math.arizona.edu/anewell/publications/201newell.pdf and https://www.biorxiv.org/content/10.1101/2023.02.13.528401v1.full.pdf. ↩
11. The nautilus shell is a logarithmic spiral whose growth ratio clusters away from the golden ratio; the "golden spiral nautilus" is an idealization. See George Markowsky, "Misconceptions about the Golden Ratio," The College Mathematics Journal 23(1), 1992: http://www.umcs.maine.edu/~markov/GoldenRatio.pdf. ↩
12. Claims that the Parthenon and Great Pyramid were designed on the golden ratio lack reliable documentary support and depend on selective measurement. See Markowsky (1992): http://www.umcs.maine.edu/~markov/GoldenRatio.pdf. ↩
13. Exponential cost of naive recursive Fibonacci ($\sim {\phi }^n$); linear iteration; logarithmic matrix exponentiation. See: https://www.cs.cornell.edu/courses/cs2022/2010sp/fibonacci.pdf and https://cp-algorithms.com/algebra/fibonacci-numbers.html. ↩
14. Matrix exponentiation by repeated squaring computes $F_n$ in $O(logn)$ matrix multiplications. See: https://cp-algorithms.com/algebra/fibonacci-numbers.html. ↩
15. Fibonacci numbers have $\Theta \left(n\right)$ digits, so big-integer arithmetic cost affects all methods. See: https://www.cs.cornell.edu/courses/cs2022/2010sp/fibonacci.pdf. ↩
16. Internal Odisena canonical source (privacy-safe): staged evidence-cycle migration rather than an all-at-once cutover. See Appendix I, items 1 and 7. ↩
17. Bounded advanced example (established methods, not novel physics): at each cycle, load and verify the last accepted checkpoint (hash, units, validity), failing closed if it cannot be verified. See Appendix I, item 11; underlying quantum-filtering methods cited at note [^ch24-quantum]. ↩
18. Internal Odisena canonical source (privacy-safe): the cycle-boundary halt requires the previous cycle's log before the next attempt begins. See Appendix I, item 6. ↩
19. Extension to negative indices: $F_{-n}=(-1{)}^{n+1}{F}_n$. See: https://en.wikipedia.org/wiki/Fibonacci_sequence and https://oeis.org/A000045. ↩
20. Fibonacci numbers modulo $m$ are periodic (the Pisano period). See: https://mathworld.wolfram.com/PisanoPeriod.html and https://oeis.org/A001175. ↩
21. Internal Odisena canonical source (privacy-safe): the fielded subdomain constellation assigning distinct scope and audience to each surface, isolating experimental surfaces. See Appendix I, item 5. ↩
22. Internal Odisena canonical source (privacy-safe): item-level, classification-aware, validation-gated public release. See Appendix I, item 9. ↩
23. Cassini's identity as an independent invariant/validator. See: https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities. ↩
24. Fibonacci summation, sum-of-squares, and addition formulas. See: https://mathworld.wolfram.com/FibonacciNumber.html and https://oeis.org/A000045. ↩
25. Internal Odisena canonical source (privacy-safe): the governance chain preserves predecessor amendments verbatim while advancing the chain head. See Appendix I, item 3. ↩
26. Lucas numbers: same recurrence, base cases $L_0=2,L_1=1$; $L_n=F_{n-1}+F_{n+1}$. See: https://oeis.org/A000032 and https://mathworld.wolfram.com/LucasNumber.html. ↩
27. Bounded advanced example: the assumption set (model family, measurement convention, precision, state assumptions) is versioned; an assumption change creates a new branch, not a rewrite. See Appendix I, item 11; methods cited at [^ch24-quantum]. ↩
28. Internal Odisena canonical source (privacy-safe): pre-declared irrecoverable criteria, preserved partial state, and a waiting period before an irrecoverable call. See Appendix I, item 6. ↩
29. Internal Odisena canonical source (privacy-safe): recovery plan mapping each step to RFPA moves and AVPT beats with explicit anti-pattern gates. See Appendix I, item 6. ↩
30. Internal Odisena canonical source (privacy-safe): the fleet AVPT CI/CD rollout marked dry-run/non-destructive and SHA-pinned so attempts are not mistaken for accepted production states. See Appendix I, item 4. Public repository context, where already public and safe: https://github.com/iwdansereau-ops/odisena-console/pull/14. ↩
31. Cassini's identity as an independent check catching errors the recurrence check would miss. See: https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities. ↩
32. Binet approximation as a sanity bound. See: https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html. ↩
33. Bounded advanced example: a battery of independent gates (numerical, physicality, innovation-distribution, predictive-calibration, identifiability); promote only if all pass, else roll back or quarantine. See Appendix I, item 11; methods cited at [^ch24-quantum]. ↩
34. Internal Odisena canonical source (privacy-safe): AI outputs treated as validation-gated, not authorization-gated. See Appendix I, item 9. ↩
35. Bounded advanced example: append-only cycle artifact (cycle id, parent hash, timestamps, inputs/outputs, validation metrics, decision, own hash), with raw data immutable and derived states regenerable. See Appendix I, item 11; methods cited at [^ch24-quantum]. ↩
36. Internal Odisena canonical source (privacy-safe): predecessor amendments preserved verbatim; tracker/dashboard artifacts regenerated, not patched. See Appendix I, item 3. ↩
37. Internal Odisena canonical source (privacy-safe): a stale expansion in creative work was corrected via an explicit correction log rather than a silent edit. See Appendix I, items 1 and 12. ↩
38. Internal Odisena canonical source (privacy-safe): numbered ratification receipts and versioned registries recording deltas and preserving prior-version states. See Appendix I, items 3 and 12. ↩
39. Internal Odisena canonical source (privacy-safe): a receipt-number collision resolved by an explicit collision-correction event and a new registry version, never a silent renumber. See Appendix I, item 12. ↩
40. Internal Odisena canonical source (privacy-safe): production promotion kept distinct from code merge, fail-closed until preservation infrastructure exists. See Appendix I, item 4. ↩
41. Internal Odisena canonical source (privacy-safe): governed promotion fail-closed boundary — production restored to disabled until buckets, roles, and ledger evidence exist. See Appendix I, item 5. ↩
42. Internal Odisena canonical source (privacy-safe): a supersession note attached alongside a versioned file, marking one affected clause, carrying the fix into the next full regeneration, and preserving the predecessor marked-superseded. See Appendix I, item 12. ↩
43. Internal Odisena canonical source (privacy-safe): the AVPT CI/CD dashboard — webhook receiver, durable ledger, observability stack, reusable workflow, snapshot adapters, and an AVPT-versus-linear comparison view. See Appendix I, item 4. ↩
44. The distinction between an infinite sequence and a non-terminating computation; the halting problem. See: https://en.wikipedia.org/wiki/Halting_problem and https://plato.stanford.edu/entries/turing-machine/. ↩
45. Internal Odisena canonical source (privacy-safe): the recursive-continuation ("infinity–mind–infinity") state is registered as a governed state requiring canon review, evidence preservation, and explicit supersession. See Appendix I, item 1. ↩
46. Internal Odisena canonical source (privacy-safe): a migration loop went to a hard hold after repeated baseline-capture failure and refused to arm the next cycle until missing evidence was verified. See Appendix I, item 7. ↩
47. Internal Odisena canonical source (privacy-safe): snapshot-first cadence — preserve pre-deployment state before canary rollout; track rollback and drift. See Appendix I, item 4. ↩
48. Internal Odisena canonical source (privacy-safe): preserve the highest partial state so a failed attempt can be reversed to a known point. See Appendix I, item 6. ↩
49. Internal Odisena canonical source (privacy-safe): "regenerate, don't patch" — predecessor amendments preserved verbatim; derived views regenerated. See Appendix I, item 3. ↩
50. Internal Odisena canonical source (privacy-safe): three-replica knowledge sync via a deterministic engine; a scheduled runner made to invoke one executable so orchestration cannot override a clean no-op. See Appendix I, item 9. ↩
51. Second-order linear recurrences as a family: Lucas, Pell, and generalized sequences share the shape and its guarantees. See: https://oeis.org/wiki/Index_to_OEIS:_Section_Fi and https://oeis.org/A000129 (Pell). ↩
52. Internal Odisena canonical source (privacy-safe, doctrine): the Founding Loop — collapse possibility into one buildable loop, then scale a proven loop into repeatable variants; canonical glyph string quoted as an artifact and explained in plain language. See Appendix I, item 2. ↩
53. Internal Odisena canonical source (privacy-safe): a shared reusable workflow instantiated across repositories via per-repository callers, rolled out inert first. See Appendix I, item 4. ↩
54. Internal Odisena canonical source (privacy-safe): the seven-layer socio-technical system with a governance layer running through all layers; explicitly not a single ML model; broad authorization does not permit exposing classified items. See Appendix I, item 9. ↩
55. Dynamic programming: optimal substructure and overlapping subproblems; memoization vs. tabulation. See: https://en.wikipedia.org/wiki/Dynamic_programming and https://cp-algorithms.com/algebra/fibonacci-numbers.html. ↩
56. The number of domino tilings of a $2\times n$ board is $F_{n+1}$. See: https://www.cut-the-knot.org/arithmetic/combinatorics/FibonacciTilings.shtml. ↩
57. Event sourcing: current state derived by replaying an append-only event log; versioned infrastructure and reversible migrations. See: https://martinfowler.com/eaaDev/EventSourcing.html. ↩
58. Internal Odisena canonical source (privacy-safe): durable ledger, snapshot adapters, and a recovery-time comparison view. See Appendix I, item 4. ↩
59. Internal Odisena canonical source (privacy-safe): production promotion fail-closed and separate from code merge. See Appendix I, item 5. ↩
60. Bounded advanced example (established methods, not novel physics): a governed recursive estimator for a one-dimensional Gaussian quantum state under continuous weak measurement, built on the stochastic master equation, Gaussian moment closure, the Riccati covariance equation, and the quantum Kalman/Kalman–Bucy structure. Underlying peer-reviewed and preprint methods include: conditional Gaussian quantum dynamics https://arxiv.org/abs/1607.02619; the quantum extended Kalman filter https://arxiv.org/abs/1603.01890; the Robertson–Schrödinger uncertainty relation https://iopscience.iop.org/article/10.1088/1361-6404/abd98a; single-shot continuous-measurement parameter estimation https://arxiv.org/abs/0811.0601; Gaussian trajectories under quadratic dynamics https://iopscience.iop.org/article/10.1088/1751-8121/ac9d73; and the continuous-measurement Cramér–Rao bound https://arxiv.org/abs/1608.08429. The RFPA/AVPT governance layer around these established methods is presented as an architecture, not as new physics, and makes no claim to invalidate any established principle. See Appendix I, item 11. ↩
61. Internal Odisena canonical source (privacy-safe): item-level, validation-gated release of AI-assisted outputs. See Appendix I, item 9. ↩
62. KDP paperback interior margin (gutter) requirements by page count and minimum outside margin (official KDP help): https://kdp.amazon.com/help/topic/GVBQ3CMEQW3W2VL6. ↩
63. KDP cover spine-width formula (white paper: page count × 0.002252″), bleed, and safe-area requirements (official KDP help): https://kdp.amazon.com/help/topic/G201857950 and the KDP Cover Calculator: https://kdp.amazon.com/cover-calculator. ↩
64. Phyllotaxis, the golden angle, and Douady–Couder experiments. See: https://archive.math.arizona.edu/anewell/publications/201newell.pdf and https://www.biorxiv.org/content/10.1101/2023.02.13.528401v1.full.pdf. ↩
65. The nautilus is not a golden spiral. See Markowsky (1992): http://www.umcs.maine.edu/~markov/GoldenRatio.pdf. ↩
66. Golden-ratio design claims for the Parthenon and pyramids are unsupported/retrofitted. See Markowsky (1992): http://www.umcs.maine.edu/~markov/GoldenRatio.pdf. ↩
67. Experimental evidence for a preference for golden-ratio rectangles is weak and mixed. See Markowsky (1992): http://www.umcs.maine.edu/~markov/GoldenRatio.pdf. ↩
68. Internal Odisena canonical source (privacy-safe): numbered receipts, versioned registries, and supersession notes as institutional memory. See Appendix I, items 3 and 12. ↩
69. Internal Odisena canonical source (privacy-safe): a supersession note marking one clause superseded while preserving the rest. See Appendix I, item 12. ↩
70. Internal Odisena canonical source (privacy-safe): a collision correction preserving the authoritative chain, keeping the colliding artifact as an inert record, refiling the correction, and advancing the registry, with the rule that no artifact is deleted or silently rewritten. See Appendix I, item 12. ↩
71. On-Line Encyclopedia of Integer Sequences, A000045 (Fibonacci numbers): https://oeis.org/A000045. ↩
72. Binet's formula. See: https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html. ↩
73. Cassini's identity. See: https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities. ↩
74. The GCD property $gcd(F_m,F_n)=F_{gcd(m,n)}$. See: https://mathworld.wolfram.com/FibonacciNumber.html. ↩
75. Convergence of ratios to $\phi$. See: https://oeis.org/A000045. ↩
76. Binet's formula via the characteristic equation. See: https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html. ↩
77. Cassini's identity via the Q-matrix determinant. See: https://www.cut-the-knot.org/arithmetic/algebra/FibonacciMatrix.shtml. ↩
78. Complexity of Fibonacci algorithms. See: https://www.cs.cornell.edu/courses/cs2022/2010sp/fibonacci.pdf. ↩
79. Domino-tiling interpretation. See: https://www.cut-the-knot.org/arithmetic/combinatorics/FibonacciTilings.shtml. ↩
80. KDP margins/gutter by page count (official KDP help): https://kdp.amazon.com/help/topic/GVBQ3CMEQW3W2VL6. ↩
81. KDP paperback submission guidelines — embedded fonts, ≥300 DPI, single pages, spine formula, bleed, safe area, barcode (official KDP help): https://kdp.amazon.com/help/topic/G201857950. Print trim sizes: https://kdp.amazon.com/help/topic/G201834180. Print options overview: https://kdp.amazon.com/help/topic/G200645680. ↩