Pith Number

pith:2TPB73CK

pith:2013:2TPB73CKCTRNAHGEIV2RTAUYF7

not attested not anchored not stored refs pending

Algebraic Birkhoff Factorization and the Euler-Maclaurin Formula on Cones

Bin Zhang, Li Guo, Sylvie Paycha

arxiv:1306.3420 v4 · 2013-06-14 · math-ph · math.CO · math.MP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2TPB73CKCTRNAHGEIV2RTAUYF7}

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	2026-05-18T00:49:52.909447Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4de1fec4a14e2d01cc445751982982ffb7c2a545b748d07f7c0de8f0f5e8f97

Aliases

arxiv: 1306.3420 · arxiv_version: 1306.3420v4 · doi: 10.48550/arxiv.1306.3420 · pith_short_12: 2TPB73CKCTRN · pith_short_16: 2TPB73CKCTRNAHGE · pith_short_8: 2TPB73CK

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/2TPB73CKCTRNAHGEIV2RTAUYF7 \
  | 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: d4de1fec4a14e2d01cc445751982982ffb7c2a545b748d07f7c0de8f0f5e8f97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e304c22c6009097ec71d614d3bf101aa612776d1df64bc76c04062d7badff4e",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-06-14T15:09:52Z",
    "title_canon_sha256": "655452f884da8ed962b1e185b829f06ea9bca553c54ab7999176b126939089f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3420",
    "kind": "arxiv",
    "version": 4
  }
}