Pith Number

pith:752LTVIS

pith:2016:752LTVIS5B3QMYK2UASRO74HKO

not attested not anchored not stored refs pending

Group trisections and smooth 4-manifolds

Aaron Abrams, David T. Gay, Robion Kirby

arxiv:1605.06731 v1 · 2016-05-22 · 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{752LTVIS5B3QMYK2UASRO74HKO}

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	2026-05-18T00:20:07.559035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff74b9d512e87706615aa025177f87539d8f7f83ad137586cc84275e0d712878

Aliases

arxiv: 1605.06731 · arxiv_version: 1605.06731v1 · doi: 10.48550/arxiv.1605.06731 · pith_short_12: 752LTVIS5B3Q · pith_short_16: 752LTVIS5B3QMYK2 · pith_short_8: 752LTVIS

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/752LTVIS5B3QMYK2UASRO74HKO \
  | 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: ff74b9d512e87706615aa025177f87539d8f7f83ad137586cc84275e0d712878

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "411c58e0219291e67f6b5fddc58358b6387c76bedeecedada4353e3de3f901a1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-05-22T03:49:00Z",
    "title_canon_sha256": "2d9f97bfb272ee31ddf96ff777f8cef5c813fe19b916ce048edae9fcf62a79fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06731",
    "kind": "arxiv",
    "version": 1
  }
}