Pith Number

pith:AXAYGI7N

pith:2011:AXAYGI7NJPRZB7XGWW2WHDTPO7

not attested not anchored not stored refs pending

Fibonacci-like growth of numerical semigroups of a given genus

Alex Zhai

arxiv:1111.3142 v1 · 2011-11-14 · 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{AXAYGI7NJPRZB7XGWW2WHDTPO7}

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	2026-05-18T04:08:22.911387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05c18323ed4be390fee6b5b5638e6f77ff21744fa20b7b9c90cc1019744c0b44

Aliases

arxiv: 1111.3142 · arxiv_version: 1111.3142v1 · doi: 10.48550/arxiv.1111.3142 · pith_short_12: AXAYGI7NJPRZ · pith_short_16: AXAYGI7NJPRZB7XG · pith_short_8: AXAYGI7N

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/AXAYGI7NJPRZB7XGWW2WHDTPO7 \
  | 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: 05c18323ed4be390fee6b5b5638e6f77ff21744fa20b7b9c90cc1019744c0b44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26a7366763933d7ef7bb6c1ff88884ef570ee204ef4ebd5ee499aa23ca6c7058",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-14T08:57:10Z",
    "title_canon_sha256": "2e9da7be936c058a9eafb2c26077923a8f103fba2eb55b8a8d2c1014e01c8f03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3142",
    "kind": "arxiv",
    "version": 1
  }
}