Pith Number

pith:ILCRJDV6

pith:2024:ILCRJDV6GDJWSC5CU4KN4AOCTX

not attested not anchored not stored refs pending

The Thurston norm of graph manifolds

Alessandro V. Cigna

arxiv:2412.03437 v2 · 2024-12-04 · 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{ILCRJDV6GDJWSC5CU4KN4AOCTX}

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	2026-07-05T11:19:22.831364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42c5148ebe30d3690ba2a714de01c29dfda8e131e02c4d97651687b472f7cb65

Aliases

arxiv: 2412.03437 · arxiv_version: 2412.03437v2 · doi: 10.48550/arxiv.2412.03437 · pith_short_12: ILCRJDV6GDJW · pith_short_16: ILCRJDV6GDJWSC5C · pith_short_8: ILCRJDV6

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/ILCRJDV6GDJWSC5CU4KN4AOCTX \
  | 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: 42c5148ebe30d3690ba2a714de01c29dfda8e131e02c4d97651687b472f7cb65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f1bc6db13a778e780e14be4a3d535e1987ebfdadd562faaa76fe098b050be48",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2024-12-04T16:27:56Z",
    "title_canon_sha256": "68825efc870a88a03e228a14f5f2863469ca11d3d509e6730ef06f7d83801d46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03437",
    "kind": "arxiv",
    "version": 2
  }
}