Pith Number

pith:WPANGDDT

pith:2021:WPANGDDT2DXO2UW2OSTAIV2UF4

not attested not anchored not stored refs pending

Minimal volume entropy and fiber growth

Ivan Babenko, St\'ephane Sabourau

arxiv:2102.04551 v2 · 2021-02-08 · 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{WPANGDDT2DXO2UW2OSTAIV2UF4}

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.

Cited by

1 paper in Pith

Topological volumes of certain complete affine manifolds

Receipt and verification

First computed	2026-07-05T08:11:49.152449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3c0d30c73d0eeed52da74a60457542f2e98bf3c1d3256926ec8c49933291e87

Aliases

arxiv: 2102.04551 · arxiv_version: 2102.04551v2 · doi: 10.48550/arxiv.2102.04551 · pith_short_12: WPANGDDT2DXO · pith_short_16: WPANGDDT2DXO2UW2 · pith_short_8: WPANGDDT

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/WPANGDDT2DXO2UW2OSTAIV2UF4 \
  | 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: b3c0d30c73d0eeed52da74a60457542f2e98bf3c1d3256926ec8c49933291e87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b71853f65e980f189e35c7a985c3b5b538b83f4b04293c81834e464b7167c3a8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-02-08T22:03:46Z",
    "title_canon_sha256": "a7bdc9006f9609d148134507a1c0ad084e850bf98c0faeff7e83e4caf4ca4bf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.04551",
    "kind": "arxiv",
    "version": 2
  }
}