Pith Number

pith:VTBTPLGO

pith:2012:VTBTPLGOW5PSUEQHIKMNED4BGZ

not attested not anchored not stored refs pending

Updown categories: Generating functions and universal covers

Michael E. Hoffman

arxiv:1207.1705 v1 · 2012-07-06 · 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{VTBTPLGOW5PSUEQHIKMNED4BGZ}

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	2026-05-18T01:21:03.159056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acc337acceb75f2a12074298d20f813655c38f036071e9285e47644b5419c72f

Aliases

arxiv: 1207.1705 · arxiv_version: 1207.1705v1 · doi: 10.48550/arxiv.1207.1705 · pith_short_12: VTBTPLGOW5PS · pith_short_16: VTBTPLGOW5PSUEQH · pith_short_8: VTBTPLGO

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/VTBTPLGOW5PSUEQHIKMNED4BGZ \
  | 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: acc337acceb75f2a12074298d20f813655c38f036071e9285e47644b5419c72f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87f5a5922558d0d400f020e97e8d84b312526984184f18516676d0316d40d290",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-06T18:58:55Z",
    "title_canon_sha256": "a4c84c9a9d42a18c14b1b3a4a4ba62f766219ee4ea7303ca1d9cf4b0cef4720a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1705",
    "kind": "arxiv",
    "version": 1
  }
}