Pith Number

pith:YWMBU6CV

pith:2011:YWMBU6CVWU2JMUSKLBX6EEWPKX

not attested not anchored not stored refs pending

Embedding universal covers of graph manifolds in products of trees

Alessandro Sisto, David Hume

arxiv:1112.0263 v2 · 2011-12-01 · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YWMBU6CVWU2JMUSKLBX6EEWPKX}

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	2026-05-18T03:57:40.404965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5981a7855b53496524a586fe212cf55db2c43cdc3d80a33bdc219b039fb11bb

Aliases

arxiv: 1112.0263 · arxiv_version: 1112.0263v2 · doi: 10.48550/arxiv.1112.0263 · pith_short_12: YWMBU6CVWU2J · pith_short_16: YWMBU6CVWU2JMUSK · pith_short_8: YWMBU6CV

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/YWMBU6CVWU2JMUSKLBX6EEWPKX \
  | 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: c5981a7855b53496524a586fe212cf55db2c43cdc3d80a33bdc219b039fb11bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3107b8ec0ecfa803b934d90b27fbc861d5670d813467b0b5b3a771aadb53a1cb",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-01T18:31:51Z",
    "title_canon_sha256": "0e88b2ca332ae8c660514acb1a8318f4497d3082bc665fa17cc1619010367639"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0263",
    "kind": "arxiv",
    "version": 2
  }
}