Pith Number

pith:PTJS5TF4

pith:2018:PTJS5TF4B7IHEICUZCWWW75DCT

not attested not anchored not stored refs pending

A counterexample to a strong version of the Andrews-Curtis conjecture

Jonathan Ariel Barmak

arxiv:1806.11493 v1 · 2018-06-29 · math.AT · math.GR · math.GT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTJS5TF4B7IHEICUZCWWW75DCT}

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	2026-05-18T00:12:01.711801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cd32eccbc0fd0722054c8ad6b7fa314f69ef24ecc748130b99a32f68ad6f6e4

Aliases

arxiv: 1806.11493 · arxiv_version: 1806.11493v1 · doi: 10.48550/arxiv.1806.11493 · pith_short_12: PTJS5TF4B7IH · pith_short_16: PTJS5TF4B7IHEICU · pith_short_8: PTJS5TF4

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/PTJS5TF4B7IHEICUZCWWW75DCT \
  | 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: 7cd32eccbc0fd0722054c8ad6b7fa314f69ef24ecc748130b99a32f68ad6f6e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a690ae7fd89cb1221fc42d0c95f1804a0ce2b0afec1661acca8513fceb4df4b",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-06-29T15:52:07Z",
    "title_canon_sha256": "d4cf557ac3e2a5790796e331a1d59cc61a6323f2cf089d1c3ed336f009528e2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.11493",
    "kind": "arxiv",
    "version": 1
  }
}