PROVED
Exact identities and unconditional theorems as stated or cited in the volume. The first source rung W1 has an analytic proof.
Volume I · The Reading Volume
Triangular-n Postmaster.
From the triangular primitive to the completed source frontier.
DOCUMENT v4.790 PAGESSEPTEMBER 12, 2026RH STATUS: OPEN
A familiar triangle.
A precise question.
The volume begins with triangular numbers and a signed Pascal grid, then follows those exact constructions into the completed Riemann zeta source.
This page is a reading guide, not a replacement for the paper or an independent verification of its proofs. It follows the supplied v4.7 front matter, status table and reading map.
Tn = n(n + 1) / 2
triangular coordinate
q = s(1 − s)
reflection fold
triangular coordinate
q = s(1 − s)
reflection fold
The link is an exact coordinate identity. It does not, by itself, force the zeros onto the critical line.
The guide's shortest route: begin with “Start here,” then read Part IV, especially R12. That section controls rung status; R23 identifies the source statement still missing.
Root to frontier
Six entrances to the Reading Volume.
Links use physical PDF page numbers; the printed page and section labels are also given. Some phone PDF viewers ignore page fragments, so the section name is retained.
Start hereA familiar triangle, its signed rows and what the volume is asking.Front matter, printed pp. 1-7 · PDF page 4Build the triangular coordinateThe discrete primitive, reflection and the half-step.Part I, sections R1-R5E · PDF page 10Follow the complex foldReflection, conjugation and the completed resolvent.Parts II-III, sections R6-R10B · PDF page 21Read the Widder ladderThe exact rows, shifted-resolvent basis and controlling status table.Part IV, especially section R12 · PDF page 37Reach the source-energy constructionLi data, the Gamma-prime split and fixed-scale source energy.Part V, sections R15-R17I · PDF page 52Find the research boundaryResults with quantifiers, the first unsupported line and the proof map.Part VII, sections R22-R24 · PDF page 79
The volume's own status vocabulary
What is established.
What is still required.
CERTIFIED
Finite statements with their certificate inputs and quantifiers. W2-W6 are certified from the source; a much larger finite rung range uses the verified-height channel.
RH-EQUIVALENT
A full criterion logically equivalent to RH, with all of its quantifiers. An equivalence is not a proof that the criterion holds.
OPEN
The independent source route begins its next open step at W7. The full all-order fixed-scale prime estimate, and therefore the RH-closing source argument, remain unproved.
EVIDENCE
Numerical or empirical support only. It does not upgrade a mathematical status.
Read the quantifiers, not just the badge. The source-proof channel and the truth of a zero-assisted sign are different questions. Finite certified ranges, however large, are not all-order proofs. This website update did not re-execute the historical certificates.
Keep versions distinct
The document and its record.
The attached PDF identifies itself as Reading Volume v4.7. The attached PDF identifies itself as Reading Volume v4.7, dated 15 September 2026. Zenodo record 22772092 is the author-supplied publication link. The PDF cover uses “Triangular Primitive”; the repository-facing title retains “Discrete Primitive.”
The Reading Volume refers to a separate Technical Dossier. That file was not supplied for this website update; the repository record is the route to the rest of the publication materials.
Huckstead, Jeffery. Triangular-n Postmaster: From the Triangular Primitive to the Completed Source Frontier. Volume I - The Reading Volume, v4.7. Cerebral Graphix, 15 September 2026. Associated repository record: 10.5281/zenodo.22772092. ORCID: 0009-0007-0234-2177.
Read back into the trail
Earlier volumes & analytic companions.
Publication lineage and comparison models are not interchangeable with a completed-source proof.
AFTER JULY 31
Triangular n Postmaster Research Volume I v0.5: Definitive Master Union
An earlier Postmaster synthesis preserving source layers, arithmetic gates and an audited research ledger. Read for the development trail; use v4.7 for the current reading route and status table.
10.5281/zenodo.21968858
AFTER JULY 31
Triangular n Master Volume
A master-volume stage joining counting and spectral constructions with reciprocal coordinates and finite-resource comparisons. It separates exact bridges from unproved positivity targets.
10.5281/zenodo.21915297
AFTER JULY 31
Counting, Positive Degree, Reciprocal Uniformization, and Mellin-Fourier Reflection of a Spherical Casimir Spectrum
A spherical Casimir construction linking positive degree, reflection, determinants and Mellin-Fourier coordinates. Its operator and comparison models are not identified with the completed zeta source.
10.5281/zenodo.21874657
AFTER JULY 31
Two-Term Asymptotics for the Total Variation of Exponentially Weighted Laguerre Polynomials
Two-term asymptotics for the total variation of exponentially weighted Laguerre polynomials, with a Bessel-profile leading constant and a stated correction.
10.5281/zenodo.21861619