Pith Number

pith:Z5XWXXIE

pith:2002:Z5XWXXIEEUXX3W4UATB62XD7FA

not attested not anchored not stored refs pending

Heat kernel expansions on the integers

F. Alberto Grunbaum, Plamen Iliev

arxiv:math/0206089 v1 · 2002-06-09 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5XWXXIEEUXX3W4UATB62XD7FA}

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	2026-05-18T03:57:13.185477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf6f6bdd04252f7ddb9404c3ed5c7f282f4135df2bae95ede1ec240230f40b8a

Aliases

arxiv: math/0206089 · arxiv_version: math/0206089v1 · doi: 10.48550/arxiv.math/0206089 · pith_short_12: Z5XWXXIEEUXX · pith_short_16: Z5XWXXIEEUXX3W4U · pith_short_8: Z5XWXXIE

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/Z5XWXXIEEUXX3W4UATB62XD7FA \
  | 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: cf6f6bdd04252f7ddb9404c3ed5c7f282f4135df2bae95ede1ec240230f40b8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b34eb949fec097759af2491cf77dd781ed862ea456b2c295ff7b67aae4cdb12b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2002-06-09T22:42:00Z",
    "title_canon_sha256": "a30a448c5854a49ad13fd77d8e5b2bb860b36c22181a25e0b7f58e946e937648"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0206089",
    "kind": "arxiv",
    "version": 1
  }
}