Pith Number

pith:RMTWJ5FU

pith:2011:RMTWJ5FU2YXUB3CMC2UYEIU4DU

not attested not anchored not stored refs pending

A symmetric quantum calculus

Artur M. C. Brito da Cruz, Delfim F. M. Torres, Natalia Martins

arxiv:1112.6133 v1 · 2011-12-28 · 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{RMTWJ5FU2YXUB3CMC2UYEIU4DU}

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	2026-05-18T03:12:46.635231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b2764f4b4d62f40ec4c16a982229c1d19b87cd412c81b831ac246642f002432

Aliases

arxiv: 1112.6133 · arxiv_version: 1112.6133v1 · doi: 10.48550/arxiv.1112.6133 · pith_short_12: RMTWJ5FU2YXU · pith_short_16: RMTWJ5FU2YXUB3CM · pith_short_8: RMTWJ5FU

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/RMTWJ5FU2YXUB3CMC2UYEIU4DU \
  | 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: 8b2764f4b4d62f40ec4c16a982229c1d19b87cd412c81b831ac246642f002432

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33961bd33a1dfe5b5e21833ac098c851525fc3d48c425e67713de0aea2a9d0c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-12-28T15:14:17Z",
    "title_canon_sha256": "537b9f700ccebcf53e72f4008ff8096be8d5eee1e23c0c7853d398b69164ca0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6133",
    "kind": "arxiv",
    "version": 1
  }
}