Pith Number

pith:S556K7H3

pith:2026:S556K7H3KDJ4ZS4JSDVP2OX64A

not attested not anchored not stored refs pending

A Fibonacci theorem for Collatz trajectories via modular graph structure

Manuel-Alejandro Reyes Jim\'enez

arxiv:2606.02621 v1 · 2026-05-28 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S556K7H3KDJ4ZS4JSDVP2OX64A}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-03T00:05:04.906640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

977be57cfb50d3cccb8990eafd3afee014235126c94cde839d043df673e54acb

Aliases

arxiv: 2606.02621 · arxiv_version: 2606.02621v1 · doi: 10.48550/arxiv.2606.02621 · pith_short_12: S556K7H3KDJ4 · pith_short_16: S556K7H3KDJ4ZS4J · pith_short_8: S556K7H3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/S556K7H3KDJ4ZS4JSDVP2OX64A \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 977be57cfb50d3cccb8990eafd3afee014235126c94cde839d043df673e54acb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bd63db43b52f210b8117ba648befd0b8f588e104f2baf1be47efaa6668d4975",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-28T10:58:39Z",
    "title_canon_sha256": "1bc64451e36755744128b82e1d98edbecc452f42fe8cb3e0e1a3af9d0fbe496f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02621",
    "kind": "arxiv",
    "version": 1
  }
}