Pith Number

pith:PC6JZSD7

pith:2013:PC6JZSD7KQJHNNDK3OD6SK5YVM

not attested not anchored not stored refs pending

Cheeger constants and $L^2$-Betti numbers

Lewis Bowen

arxiv:1303.5963 v4 · 2013-03-24 · 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{PC6JZSD7KQJHNNDK3OD6SK5YVM}

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	2026-05-18T01:28:15.323172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78bc9cc87f541276b46adb87e92bb8ab3708b1306e2eb93798d09d09f7ed153e

Aliases

arxiv: 1303.5963 · arxiv_version: 1303.5963v4 · doi: 10.48550/arxiv.1303.5963 · pith_short_12: PC6JZSD7KQJH · pith_short_16: PC6JZSD7KQJHNNDK · pith_short_8: PC6JZSD7

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/PC6JZSD7KQJHNNDK3OD6SK5YVM \
  | 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: 78bc9cc87f541276b46adb87e92bb8ab3708b1306e2eb93798d09d09f7ed153e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39aaf42502fc2761280fad3dce8d55833cf3f5ccbd5649f7018741551f558ca9",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-03-24T16:20:37Z",
    "title_canon_sha256": "5a1b6112e5d7db379673133779eb64e9c777d2a3d43410a72c13dea737729fa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5963",
    "kind": "arxiv",
    "version": 4
  }
}