Pith Number

pith:34R5UZUR

pith:2016:34R5UZURLFXSYFZBMZOSCZITIH

not attested not anchored not stored refs pending

A uniform asymptotic expansion for the incomplete gamma functions revisited

R B Paris

arxiv:1611.00548 v1 · 2016-11-02 · 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{34R5UZURLFXSYFZBMZOSCZITIH}

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	2026-05-18T01:00:32.451535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df23da6691596f2c1721665d21651341e0ffa04c46c655e8359521dc2b3a16b2

Aliases

arxiv: 1611.00548 · arxiv_version: 1611.00548v1 · doi: 10.48550/arxiv.1611.00548 · pith_short_12: 34R5UZURLFXS · pith_short_16: 34R5UZURLFXSYFZB · pith_short_8: 34R5UZUR

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/34R5UZURLFXSYFZBMZOSCZITIH \
  | 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: df23da6691596f2c1721665d21651341e0ffa04c46c655e8359521dc2b3a16b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc99febb8f77c442bde83f817604b79398ba17d079d3466c9849c63737366400",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-11-02T11:18:30Z",
    "title_canon_sha256": "782bba82e04dd06536aef447affce0bd5db542c85e215066d38507d5b297f619"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.00548",
    "kind": "arxiv",
    "version": 1
  }
}