Pith Number

pith:GPRKCXZG

pith:2015:GPRKCXZGZURPQMBBCHOHUJG63C

not attested not anchored not stored refs pending

Series Representation of Modified Bessel Functions and Its Application in AF Cooperative systems

Mehdi M. Molu

arxiv:1506.04283 v1 · 2015-06-13 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GPRKCXZGZURPQMBBCHOHUJG63C}

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	2026-05-18T01:49:55.026186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33e2a15f26cd22f8302111dc7a24ded8889ac27628097b6276faedd3137cdf87

Aliases

arxiv: 1506.04283 · arxiv_version: 1506.04283v1 · doi: 10.48550/arxiv.1506.04283 · pith_short_12: GPRKCXZGZURP · pith_short_16: GPRKCXZGZURPQMBB · pith_short_8: GPRKCXZG

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/GPRKCXZGZURPQMBBCHOHUJG63C \
  | 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: 33e2a15f26cd22f8302111dc7a24ded8889ac27628097b6276faedd3137cdf87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d65dfc101d25219a1d84a8a26324b62ff3a92742f5d6627477f972f261f79a8c",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-06-13T16:06:19Z",
    "title_canon_sha256": "8b65271ed94e381ec346564ba847b406289bed30abf9f18710abb6cf43189c7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04283",
    "kind": "arxiv",
    "version": 1
  }
}