Pith Number

pith:Q2YL2U7S

pith:2012:Q2YL2U7SNOLAUIN7S2WIBAKHSL

not attested not anchored not stored refs pending

A geometric criterion to be pseudo-Anosov

Christopher J. Leininger, Richard P. Kent IV

arxiv:1208.2494 v2 · 2012-08-13 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q2YL2U7SNOLAUIN7S2WIBAKHSL}

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	2026-05-18T02:54:47.266683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86b0bd53f26b960a21bf96ac80814792f48593b4d06cb70d1c8bbbeb2cd10b15

Aliases

arxiv: 1208.2494 · arxiv_version: 1208.2494v2 · doi: 10.48550/arxiv.1208.2494 · pith_short_12: Q2YL2U7SNOLA · pith_short_16: Q2YL2U7SNOLAUIN7 · pith_short_8: Q2YL2U7S

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/Q2YL2U7SNOLAUIN7S2WIBAKHSL \
  | 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: 86b0bd53f26b960a21bf96ac80814792f48593b4d06cb70d1c8bbbeb2cd10b15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86de308828ca9dcabb33449961aeed3512183577357f6be5ff9ec90c7b9f6ef8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-08-13T05:06:01Z",
    "title_canon_sha256": "09d047df4a65b9e5649bf868532c29b1e5b73c29a0e001885d701e2148879f98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2494",
    "kind": "arxiv",
    "version": 2
  }
}