Pith Number

pith:A2FCSNN7

pith:2026:A2FCSNN7M67MBQVHIY75H7ZXET

not attested not anchored not stored refs pending

Machine-checkable equivalence certificates at the length-14 Andrews-Curtis frontier

Josep Carreras

arxiv:2607.23611 v1 · 2026-07-26 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A2FCSNN7M67MBQVHIY75H7ZXET}

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	2026-07-28T01:23:01.919349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

068a2935bf67bec0c2a7463fd3ff3724f9b7d500e4fa1efc1db54ed68069ab98

Aliases

arxiv: 2607.23611 · arxiv_version: 2607.23611v1 · doi: 10.48550/arxiv.2607.23611 · pith_short_12: A2FCSNN7M67M · pith_short_16: A2FCSNN7M67MBQVH · pith_short_8: A2FCSNN7

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/A2FCSNN7M67MBQVHIY75H7ZXET \
  | 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: 068a2935bf67bec0c2a7463fd3ff3724f9b7d500e4fa1efc1db54ed68069ab98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4a1659ce97b06bda4b5463f1a4375dbe453bd2f6dec34b5ab633befe05c79e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-26T11:35:27Z",
    "title_canon_sha256": "664004309e6f1b1d914939e4f84c96382c26e1f0ef295b548bd90ee4b3870e9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23611",
    "kind": "arxiv",
    "version": 1
  }
}