Pith Number

pith:27TAGS7X

pith:2011:27TAGS7XMTZJE6YWQWO646SGPX

not attested not anchored not stored refs pending

Dual identities in fractional difference calculus within Riemann

Thabet Abdeljawad

arxiv:1112.5795 v2 · 2011-12-25 · 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{27TAGS7XMTZJE6YWQWO646SGPX}

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	2026-05-18T03:36:56.711837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e6034bf764f2927b16859dee7a467de4c8b6dee037d5e8c64a9c5cdb521dd3

Aliases

arxiv: 1112.5795 · arxiv_version: 1112.5795v2 · doi: 10.48550/arxiv.1112.5795 · pith_short_12: 27TAGS7XMTZJ · pith_short_16: 27TAGS7XMTZJE6YW · pith_short_8: 27TAGS7X

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/27TAGS7XMTZJE6YWQWO646SGPX \
  | 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: d7e6034bf764f2927b16859dee7a467de4c8b6dee037d5e8c64a9c5cdb521dd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8494d4d5b78fd8e36169c6df7bf4a41f39a9f93264ecc933c06ed99136aad9f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-25T20:59:00Z",
    "title_canon_sha256": "af3222cb085ef5bf80dba44bcb108114b8eed3d612b3c25dd259f280b73c9c1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5795",
    "kind": "arxiv",
    "version": 2
  }
}