Pith Number

pith:YMBJ2ZBP

pith:2007:YMBJ2ZBPCXGO5B3NYERTS6G6DZ

not attested not anchored not stored refs pending

Cyclic systems of simultaneous congruences

Jeffrey C. Lagarias

arxiv:0712.3954 v3 · 2007-12-23 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YMBJ2ZBPCXGO5B3NYERTS6G6DZ}

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	2026-05-18T04:34:00.823404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3029d642f15ccee876dc1233978de1e63f883e24d7dab0f326d237c0f4f748b

Aliases

arxiv: 0712.3954 · arxiv_version: 0712.3954v3 · doi: 10.48550/arxiv.0712.3954 · pith_short_12: YMBJ2ZBPCXGO · pith_short_16: YMBJ2ZBPCXGO5B3N · pith_short_8: YMBJ2ZBP

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/YMBJ2ZBPCXGO5B3NYERTS6G6DZ \
  | 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: c3029d642f15ccee876dc1233978de1e63f883e24d7dab0f326d237c0f4f748b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f902ff6d450023a4dba4e52a746e9ac5c42fb75809b0b68b99c742e6d9ab5d20",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-12-23T21:47:03Z",
    "title_canon_sha256": "58a117e66c27acbabeb6f6b15d7c8ee74cd612509bcfe2bc448a96bf05ab15ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3954",
    "kind": "arxiv",
    "version": 3
  }
}