Pith Number

pith:QUB75N36

pith:2026:QUB75N36KPO5U5TBP3AK45RQYE

not attested not anchored not stored refs pending

A Coordinate System for Collatz Dynamics

Jennifer Williams

arxiv:2607.01718 v1 · 2026-07-02 · 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{QUB75N36KPO5U5TBP3AK45RQYE}

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	2026-07-03T01:17:27.721002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8503feb77e53ddda76617ec0ae7630c137c4fca2c7cdc96c29712f283b6b8be4

Aliases

arxiv: 2607.01718 · arxiv_version: 2607.01718v1 · doi: 10.48550/arxiv.2607.01718 · pith_short_12: QUB75N36KPO5 · pith_short_16: QUB75N36KPO5U5TB · pith_short_8: QUB75N36

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/QUB75N36KPO5U5TBP3AK45RQYE \
  | 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: 8503feb77e53ddda76617ec0ae7630c137c4fca2c7cdc96c29712f283b6b8be4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c324143e2671d76f09621964df811a3847315394659311b9ec48c48911c94812",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-02T05:16:36Z",
    "title_canon_sha256": "0ac1d9cebe17237b3ac3b5ee568c67a791d14bbc1ff71df5518e9b409f251ec8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01718",
    "kind": "arxiv",
    "version": 1
  }
}