Pith Number

pith:4CH75OW3

pith:2019:4CH75OW3OB5TYOVK6R6YVDUD5C

not attested not anchored not stored refs pending

On the length of chains in a metric space

Mathav Murugan

arxiv:1909.09988 v2 · 2019-09-22 · math.PR · math.FA · 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{4CH75OW3OB5TYOVK6R6YVDUD5C}

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	2026-07-05T01:01:35.883744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e08ffebadb707b3c3aaaf47d8a8e83e8ac0d4d59ee5fbcf6e593e5ce14ea4024

Aliases

arxiv: 1909.09988 · arxiv_version: 1909.09988v2 · doi: 10.48550/arxiv.1909.09988 · pith_short_12: 4CH75OW3OB5T · pith_short_16: 4CH75OW3OB5TYOVK · pith_short_8: 4CH75OW3

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/4CH75OW3OB5TYOVK6R6YVDUD5C \
  | 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: e08ffebadb707b3c3aaaf47d8a8e83e8ac0d4d59ee5fbcf6e593e5ce14ea4024

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21b480d6bf06ed44d3c833781036c21db22db177a305940581d1a09e2eb8c328",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-09-22T11:45:07Z",
    "title_canon_sha256": "4917fda384e071466cdb4667807c810d1359b365e53e2a0ec5176b28fff66019"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.09988",
    "kind": "arxiv",
    "version": 2
  }
}