Pith Number

pith:36NDZP5O

pith:2010:36NDZP5O7KUCRU4MPKC7VPWQ5D

not attested not anchored not stored refs pending

Fine structure of the asymptotic expansion of cyclic integrals

K. K. Kozlowski

arxiv:1001.3646 v1 · 2010-01-20 · 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{36NDZP5O7KUCRU4MPKC7VPWQ5D}

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	2026-05-18T02:09:31.799814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df9a3cbfaefaa828d38c7a85fabed0e8e5759a5ecb4c33cdc02625e13ab5fb58

Aliases

arxiv: 1001.3646 · arxiv_version: 1001.3646v1 · doi: 10.48550/arxiv.1001.3646 · pith_short_12: 36NDZP5O7KUC · pith_short_16: 36NDZP5O7KUCRU4M · pith_short_8: 36NDZP5O

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/36NDZP5O7KUCRU4MPKC7VPWQ5D \
  | 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: df9a3cbfaefaa828d38c7a85fabed0e8e5759a5ecb4c33cdc02625e13ab5fb58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9a786088f96d5ab12e40d06385764c0c3366f39080baf60d86d9630bcb83a56",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-01-20T17:23:19Z",
    "title_canon_sha256": "b2d981efa97c4e84ab87de1169932021d220facaa9c724c3782f882b7a792b68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3646",
    "kind": "arxiv",
    "version": 1
  }
}