Pith Number

pith:ZC4KKLDG

pith:2001:ZC4KKLDG7JBXV2VD2LM76QNPZY

not attested not anchored not stored refs pending

Regularized traces and Taylor expansions for the heat semigroup

Iosif Polterovich, Michael Hitrik

arxiv:math/0105163 v2 · 2001-05-19 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZC4KKLDG7JBXV2VD2LM76QNPZY}

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	2026-07-04T14:35:20.615483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8b8a52c66fa437aeaa3d2d9ff41afce08ea7aec704025bc6cb31f2033ff90b0

Aliases

arxiv: math/0105163 · arxiv_version: math/0105163v2 · doi: 10.48550/arxiv.math/0105163 · pith_short_12: ZC4KKLDG7JBX · pith_short_16: ZC4KKLDG7JBXV2VD · pith_short_8: ZC4KKLDG

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/ZC4KKLDG7JBXV2VD2LM76QNPZY \
  | 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: c8b8a52c66fa437aeaa3d2d9ff41afce08ea7aec704025bc6cb31f2033ff90b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f448306b1666e1facbee369b75297ae8c2512b577f29ebb6defb3779da2ff2a6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2001-05-19T20:33:51Z",
    "title_canon_sha256": "ca3892b9b5c260fbf94feea453f58443c8c25fff6dbbd89304e3e3d643f4dfc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0105163",
    "kind": "arxiv",
    "version": 2
  }
}