Pith Number

pith:56XJUTVL

pith:2009:56XJUTVLJVQIGHJ77Q4U7WCERX

not attested not anchored not stored refs pending

The genus spectrum of a hyperbolic 3-manifold

Alan W. Reid, D. B. McReynolds

arxiv:0901.4086 v1 · 2009-01-26 · 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{56XJUTVLJVQIGHJ77Q4U7WCERX}

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	2026-05-18T00:58:55.830097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efae9a4eab4d60831d3ffc394fd8448ddfe3c3f15507879749ff9e864fc4ce6f

Aliases

arxiv: 0901.4086 · arxiv_version: 0901.4086v1 · doi: 10.48550/arxiv.0901.4086 · pith_short_12: 56XJUTVLJVQI · pith_short_16: 56XJUTVLJVQIGHJ7 · pith_short_8: 56XJUTVL

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/56XJUTVLJVQIGHJ77Q4U7WCERX \
  | 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: efae9a4eab4d60831d3ffc394fd8448ddfe3c3f15507879749ff9e864fc4ce6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3d63bc0d08f15e4ea81f27ccbdfbfb164dc3c2211c55438cfb46532a603ec0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-01-26T20:20:02Z",
    "title_canon_sha256": "e4e002d3449d2152827532471fdb859098b42eb747fcd2cf51cd19ff1dddefe4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.4086",
    "kind": "arxiv",
    "version": 1
  }
}