Pith Number

pith:5OLLC5TN

pith:2011:5OLLC5TNNLHPMDNEUT6RLLVYEJ

not attested not anchored not stored refs pending

Some asymptotics for the Bessel functions with an explicit error term

Ilia Krasikov

arxiv:1107.2007 v2 · 2011-07-11 · 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{5OLLC5TNNLHPMDNEUT6RLLVYEJ}

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.

Cited by

1 paper in Pith

Mechanistic bridges from receptors to whole-brain dynamics: mean-field reductions, validity domains, and computational trade-offs

Receipt and verification

First computed	2026-05-18T04:18:21.968552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb96b1766d6acef60da4a4fd15aeb8224419373ef9aa60ca0b99af37d1416276

Aliases

arxiv: 1107.2007 · arxiv_version: 1107.2007v2 · doi: 10.48550/arxiv.1107.2007 · pith_short_12: 5OLLC5TNNLHP · pith_short_16: 5OLLC5TNNLHPMDNE · pith_short_8: 5OLLC5TN

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/5OLLC5TNNLHPMDNEUT6RLLVYEJ \
  | 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: eb96b1766d6acef60da4a4fd15aeb8224419373ef9aa60ca0b99af37d1416276

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a858022f7426e0028ab366f71a4b8cee35aea16b8a7c8c937f6237932fccaba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-07-11T12:09:57Z",
    "title_canon_sha256": "cb95e43dae26df87fb30a1f55883015381c96bd299422fabb34a68cd60f6e722"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2007",
    "kind": "arxiv",
    "version": 2
  }
}