Pith Number

pith:P3CPBKHO

pith:2006:P3CPBKHOY3RPJPBDFZAKSTYFIH

not attested not anchored not stored refs pending

Amalgamated products and properly 3-realizable groups

A. Quintero, D. Repov\v{s}, F. F. Lasheras, M. Cardenas

arxiv:math/0609289 v1 · 2006-09-11 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P3CPBKHOY3RPJPBDFZAKSTYFIH}

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	2026-05-18T00:08:48.883246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ec4f0a8eec6e2f4bc232e40a94f0541f139bede8f7a7c4212db4c5998daf1b6

Aliases

arxiv: math/0609289 · arxiv_version: math/0609289v1 · doi: 10.48550/arxiv.math/0609289 · pith_short_12: P3CPBKHOY3RP · pith_short_16: P3CPBKHOY3RPJPBD · pith_short_8: P3CPBKHO

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/P3CPBKHOY3RPJPBDFZAKSTYFIH \
  | 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: 7ec4f0a8eec6e2f4bc232e40a94f0541f139bede8f7a7c4212db4c5998daf1b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e86d5834ffe74e3ff5c1a81aab21657016283bd08d1ad370d79156856767a83",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2006-09-11T13:51:06Z",
    "title_canon_sha256": "6763b774c1040868e852e8ffd2f526021d5de6beade2491a1625248787c0a7af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609289",
    "kind": "arxiv",
    "version": 1
  }
}