Synopsis: The s(n) Program

Date: 2026-10-01

Status: Living document, revised whenever a result lands.

Owns: The single technical account of what this project knows, how it knows it, and what it is doing next.

Evidence cutoff: Includes the independently audited T-060 global proof replay of 2026-09-30 and Session 165’s certified n=17 upper endpoint of 2026-10-01. Earlier record-state and validation revisions are retained in Session 128.

Every number here also appears in a schema-validated artifact in this repository, or is reproducible by a command given in the text, and the artifact is authoritative where the two differ. devtools.check_synopsis enforces that in the gate.

The research synopsis is organized in chapters. A link to an earlier section lands on its chapter below; open the chapter to read the section.

  1. The Program at a Glance
  2. The Program at a Glance: Current research readiness
  3. The Program at a Glance: Document Map
  4. The Program at a Glance: Refresh rule
  5. The Program at a Glance: Research Program Status and Roadmap
  6. The Program at a Glance: Results and their significance
  7. The Program at a Glance: The Program at a Glance
  8. Workflow Entry Contracts
  9. Workflow Entry Contracts: Current Handoff
  10. Workflow Entry Contracts: Previous n11 Intake and Verification
  11. Workflow Entry Contracts: Previous: Session 165 Post-optimality Overnight
  12. Workflow Entry Contracts: Previous: Session 166 n17 Route Review
  13. Workflow Entry Contracts: Result Import and Efficient Confirmation
  14. Workflow Entry Contracts: Session 168: Families, the T-007 Correction and T-087
  15. Workflow Entry Contracts: Session 169: One Record per Line for Retained Results
  16. Workflow Entry Contracts: Switching Workflows in One Session
  17. Workflow Entry Contracts: Workflow Entry Contracts
  18. Handoff Record
  19. Handoff Record: Earlier Handoffs
  20. Handoff Record: Handoff Record
  21. Handoff Record: September 10–13
  22. What Is Built
  23. What Is Built: Compiled acceleration—unbuilt, deliberately
  24. What Is Built: Reading the gate
  25. What Is Built: The exact layer—built
  26. What Is Built: The map layer—built, not admissible
  27. What Is Built: The promotion pipeline—built end to end, with the promotion itself withheld
  28. What Is Built: The proof lane—built and producing theorems
  29. What Is Built: The proposer layer—one instrument, and the interface is unbuilt
  30. What Is Built: The refinement layer—built, with a floor
  31. What Is Built: Verification Capability Ladder
  32. What Is Built: What Is Built
  33. Terminology
  34. Terminology: Assurance, Methods, and Claims
  35. Terminology: Identifiers and Control Records
  36. Terminology: Not used here
  37. Terminology: Terminology
  38. Terminology: The deliverables, and what each one currently is
  39. Terminology: The measurements
  40. Terminology: The objects
  41. Terminology: The operations
  42. Terminology: The weighted-certificate objects
  43. Terminology: Work Units and Records
  44. The Problem
  45. The Problem: The Problem
  46. The Problem: Why exactness is not optional
  47. The Lay of the Land, by n
  48. The Lay of the Land, by n: The Lay of the Land, by n
  49. n = 11, End to End
  50. n = 11, End to End: After the intake: explorations, reviews, and the settlement ladder
  51. n = 11, End to End: Identified but not pursued
  52. n = 11, End to End: n = 11, End to End
  53. n = 11, End to End: The exact n = 11 result
  54. n = 11, End to End: The first-party ladder, and where it stopped
  55. n = 11, End to End: What a proof has to do
  56. n = 11, End to End: What the external intake changed
  57. n = 11, End to End: What worked and what did not
  58. Theoretical Results
  59. Theoretical Results: Results established here
  60. Theoretical Results: Results relied on from the literature
  61. Theoretical Results: Theoretical Results
  62. The Cell Decomposition
  63. The Cell Decomposition: A cell is not a basin, and this trap has been walked into
  64. The Cell Decomposition: Nor does a point-basin classify a flat terminal component
  65. The Cell Decomposition: Setup
  66. The Cell Decomposition: Statement
  67. The Cell Decomposition: The Cell Decomposition
  68. The Cell Decomposition: The instance: Trump’s cell
  69. The Cell Decomposition: Thirty-four dimensions become one
  70. The Cell Decomposition: Two implementations, on purpose
  71. The Cell Decomposition: What “exact” does and does not mean here
  72. The Cell Decomposition: Why
  73. The Corner, and the Method It Forced
  74. The Corner, and the Method It Forced: And what it did not buy
  75. The Corner, and the Method It Forced: Other consequences
  76. The Corner, and the Method It Forced: Reproducing all of it
  77. The Corner, and the Method It Forced: The Corner, and the Method It Forced
  78. The Corner, and the Method It Forced: The measurement
  79. The Corner, and the Method It Forced: The mechanism
  80. The Corner, and the Method It Forced: The method, and what it bought
  81. The Corner, and the Method It Forced: The prediction, and what it cost to ignore
  82. The Program So Far
  83. The Program So Far: How rounds are run
  84. The Program So Far: The Program So Far
  85. The Hypothesis Registry
  86. The Hypothesis Registry: Blocked, and on what
  87. The Hypothesis Registry: Confirmed
  88. The Hypothesis Registry: Refuted, and what each refutation bought
  89. The Hypothesis Registry: The Hypothesis Registry
  90. Sessions Conducted
  91. Sessions Conducted: Sessions Conducted
  92. Experiments Conducted
  93. Experiments Conducted: Cost and provenance
  94. Experiments Conducted: Experiments Conducted
  95. Experiments Conducted: Known defects in the record
  96. Experiments Conducted: Roll-up
  97. Experiments Conducted: What the 246 rounds jointly establish
  98. The Defect Record
  99. The Defect Record: The Defect Record
  100. Where This Stands
  101. Where This Stands: Where This Stands
  102. References
  103. References: References