Pith Number

pith:2L3ULL5Q

pith:2010:2L3ULL5Q4XXVWLTSWQYZ6SCB4J

not attested not anchored not stored refs pending

A relative version of the ordinary perturbation lemma

Marco Manetti

arxiv:1002.0683 v1 · 2010-02-03 · math.KT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2L3ULL5Q4XXVWLTSWQYZ6SCB4J}

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	2026-05-18T03:45:42.134511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2f745afb0e5ef5b2e72b4319f4841e2789b96bf78a4b1d0cc18ff0f50d0ab63

Aliases

arxiv: 1002.0683 · arxiv_version: 1002.0683v1 · doi: 10.48550/arxiv.1002.0683 · pith_short_12: 2L3ULL5Q4XXV · pith_short_16: 2L3ULL5Q4XXVWLTS · pith_short_8: 2L3ULL5Q

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/2L3ULL5Q4XXVWLTSWQYZ6SCB4J \
  | 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: d2f745afb0e5ef5b2e72b4319f4841e2789b96bf78a4b1d0cc18ff0f50d0ab63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "729f0aeb446032fd34ed07f4d7fd2a8fadfeaf3dd91a318717c380c96d63e5d0",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2010-02-03T09:59:21Z",
    "title_canon_sha256": "609c25802b0e64095376095db1b54f3bb41f7855001468afbbd9ba785d01dc12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.0683",
    "kind": "arxiv",
    "version": 1
  }
}