Pith Number

pith:L64RZTDO

pith:2016:L64RZTDOJZB6WHTBJA3XBMC6UP

not attested not anchored not stored refs pending

Cubulating random groups in the square model

Tomasz Odrzyg\'o\'zd\'z

arxiv:1610.03376 v1 · 2016-10-09 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L64RZTDOJZB6WHTBJA3XBMC6UP}

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	2026-05-18T01:02:31.657030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fb91ccc6e4e43eb1e61483770b05ea3f9a0bcd651ec90c6fd08dde34de850bc

Aliases

arxiv: 1610.03376 · arxiv_version: 1610.03376v1 · doi: 10.48550/arxiv.1610.03376 · pith_short_12: L64RZTDOJZB6 · pith_short_16: L64RZTDOJZB6WHTB · pith_short_8: L64RZTDO

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/L64RZTDOJZB6WHTBJA3XBMC6UP \
  | 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: 5fb91ccc6e4e43eb1e61483770b05ea3f9a0bcd651ec90c6fd08dde34de850bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9901798f7280f94e7ec796ef8c65499aec1cb44006e37126b5394537593144e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-10-09T18:13:13Z",
    "title_canon_sha256": "d845032c3c4205712af4e8d280b087a9b7de23a7705f6d8e903ef5fd4bded752"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03376",
    "kind": "arxiv",
    "version": 1
  }
}