Pith Number

pith:PABTZAFI

pith:2009:PABTZAFICXQM2INSFMBKNPJSOX

not attested not anchored not stored refs pending

An extension of the associated rational functions on the unit circle

K. Deckers, L. Moral, L. Velazquez, M. J. Cantero

arxiv:0911.1657 v2 · 2009-11-09 · 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{PABTZAFICXQM2INSFMBKNPJSOX}

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	2026-05-18T04:41:36.761474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78033c80a815e0cd21b22b02a6bd3275e573211ee68ea0f2c50222bf20b78070

Aliases

arxiv: 0911.1657 · arxiv_version: 0911.1657v2 · doi: 10.48550/arxiv.0911.1657 · pith_short_12: PABTZAFICXQM · pith_short_16: PABTZAFICXQM2INS · pith_short_8: PABTZAFI

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/PABTZAFICXQM2INSFMBKNPJSOX \
  | 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: 78033c80a815e0cd21b22b02a6bd3275e573211ee68ea0f2c50222bf20b78070

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75acccefe134e9b0e5a21d2428e09181ce06af7ba5254c3c90695ae3b3d950d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-11-09T12:38:39Z",
    "title_canon_sha256": "39b2382c2ec12d26270c08c555115196e93ae18f1c686627fbf039e578aafcde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1657",
    "kind": "arxiv",
    "version": 2
  }
}