Pith Number

pith:W7AC3IMC

pith:2011:W7AC3IMCUSWZ2GY5UBXGGTMK6U

not attested not anchored not stored refs pending

Arbitrarily large families of spaces of the same volume

Vincent Emery

arxiv:1107.3043 v2 · 2011-07-15 · math.GR · 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{W7AC3IMCUSWZ2GY5UBXGGTMK6U}

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	2026-05-18T03:37:53.308063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7c02da182a4ad9d1b1da06e634d8af51465e64e025ad118982c3d899eef6fdb

Aliases

arxiv: 1107.3043 · arxiv_version: 1107.3043v2 · doi: 10.48550/arxiv.1107.3043 · pith_short_12: W7AC3IMCUSWZ · pith_short_16: W7AC3IMCUSWZ2GY5 · pith_short_8: W7AC3IMC

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/W7AC3IMCUSWZ2GY5UBXGGTMK6U \
  | 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: b7c02da182a4ad9d1b1da06e634d8af51465e64e025ad118982c3d899eef6fdb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3390ecfc7aff26f2c78e06da2f1348587cbc80c29a7693e98de5f969ee9c7a17",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-15T11:12:15Z",
    "title_canon_sha256": "5629c323262119f5accf43ff8abcac4eab0ce0fd4f77abfb5652c9977ea6a533"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3043",
    "kind": "arxiv",
    "version": 2
  }
}