Pith Number

pith:YXG7CD7I

pith:2024:YXG7CD7IB5OZWXA2GMIDC7FKQT

not attested not anchored not stored refs pending

Vertex Bounds in Triangulated $d$-Manifolds and an Application to 4-Manifold Complexity

Jonathan Spreer, Lucy Tobin

arxiv:2401.11152 v2 · 2024-01-20 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YXG7CD7IB5OZWXA2GMIDC7FKQT}

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	2026-07-02T01:17:10.916476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5cdf10fe80f5d9b5c1a3310317caa84d7205c70ac2839c39811d3d94c397d66

Aliases

arxiv: 2401.11152 · arxiv_version: 2401.11152v2 · doi: 10.48550/arxiv.2401.11152 · pith_short_12: YXG7CD7IB5OZ · pith_short_16: YXG7CD7IB5OZWXA2 · pith_short_8: YXG7CD7I

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/YXG7CD7IB5OZWXA2GMIDC7FKQT \
  | 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: c5cdf10fe80f5d9b5c1a3310317caa84d7205c70ac2839c39811d3d94c397d66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b489ea2975e01282bf2559499314865dcfb268227654e4b87ed2f8e5ff6754f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-01-20T07:17:04Z",
    "title_canon_sha256": "000f55fc641fc6dfaa5821343910262786847e777e05e74d6352646741507283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.11152",
    "kind": "arxiv",
    "version": 2
  }
}