Pith Number

pith:X6S64CV5

pith:2012:X6S64CV5PI77LB5J5OKQJGGTWW

not attested not anchored not stored refs pending

Fractional differences and sums with binomial coefficients

Dumitru Baleanu, Fahd Jarad, Ravi Agarwal, Thabet Abdeljawad

arxiv:1210.0445 v1 · 2012-10-01 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6S64CV5PI77LB5J5OKQJGGTWW}

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	2026-05-18T03:44:22.450959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfa5ee0abd7a3ff587a9eb950498d3b58cdd112d085d49774a1cd5fb2a58c75b

Aliases

arxiv: 1210.0445 · arxiv_version: 1210.0445v1 · doi: 10.48550/arxiv.1210.0445 · pith_short_12: X6S64CV5PI77 · pith_short_16: X6S64CV5PI77LB5J · pith_short_8: X6S64CV5

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/X6S64CV5PI77LB5J5OKQJGGTWW \
  | 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: bfa5ee0abd7a3ff587a9eb950498d3b58cdd112d085d49774a1cd5fb2a58c75b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e56ce3c3856dbc079d3a7e3d601f0e8eff265e8bd6150ac84a79881a9f36c72f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-01T15:46:30Z",
    "title_canon_sha256": "42b0b02a63e836cd8fa4450715814e5b897b26c2c0ea96e0f6e13793de5a8313"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0445",
    "kind": "arxiv",
    "version": 1
  }
}