Pith Number

pith:ZA2S5F3W

pith:2007:ZA2S5F3WYHLC6TSJECV2V2YFPO

not attested not anchored not stored refs pending

Groups which are not properly 3-realizable

Dusan Repovs, Francisco F. Lasheras, Louis Funar

arxiv:0709.1576 v3 · 2007-09-11 · math.GT · 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{ZA2S5F3WYHLC6TSJECV2V2YFPO}

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	2026-05-18T01:17:35.596737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8352e9776c1d62f4e4920abaaeb057ba2d1035e6c3f2779e4a0c97e1001cce7

Aliases

arxiv: 0709.1576 · arxiv_version: 0709.1576v3 · doi: 10.48550/arxiv.0709.1576 · pith_short_12: ZA2S5F3WYHLC · pith_short_16: ZA2S5F3WYHLC6TSJ · pith_short_8: ZA2S5F3W

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/ZA2S5F3WYHLC6TSJECV2V2YFPO \
  | 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: c8352e9776c1d62f4e4920abaaeb057ba2d1035e6c3f2779e4a0c97e1001cce7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f33cc4ba0f092f6013c8fda4fc9e18dfaa95bab195ba2ac71cd806bed0c9aa0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2007-09-11T11:11:11Z",
    "title_canon_sha256": "8e49d106c9667fcf8d5f783b73eb4c759bd90bbc8f6c44859ed913f4fd343792"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.1576",
    "kind": "arxiv",
    "version": 3
  }
}