Pith Number

pith:VYF2IWZ5

pith:2005:VYF2IWZ5HOOROO7ZCCDTBSTLPZ

not attested not anchored not stored refs pending

Bounding volume by systoles of 3-manifolds

Mikhail G. Katz, Yuli B. Rudyak

arxiv:math/0504008 v2 · 2005-04-01 · math.DG · math.AT · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYF2IWZ5HOOROO7ZCCDTBSTLPZ}

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	2026-05-18T02:57:51.119061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749

Aliases

arxiv: math/0504008 · arxiv_version: math/0504008v2 · doi: 10.48550/arxiv.math/0504008 · pith_short_12: VYF2IWZ5HOOR · pith_short_16: VYF2IWZ5HOOROO7Z · pith_short_8: VYF2IWZ5

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/VYF2IWZ5HOOROO7ZCCDTBSTLPZ \
  | 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: ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e8da770615d27520408ffc4636f024b6d2c4e9741a64cf403edc21601ee5d5d",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT",
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2005-04-01T06:32:08Z",
    "title_canon_sha256": "86ea0c08e7ef6420ece4bcec8de643e5b6b0bc2e120e97c9cc140a00b8033aed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504008",
    "kind": "arxiv",
    "version": 2
  }
}