Pith Number

pith:HFAZY5HS

pith:2004:HFAZY5HSZITYKUXWF3PY757Y5P

not attested not anchored not stored refs pending

Equiangular Tight Frames from Paley Tournaments

Joseph M. Renes

arxiv:math/0408287 v2 · 2004-08-20 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFAZY5HSZITYKUXWF3PY757Y5P}

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	2026-05-18T03:59:12.577853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39419c74f2ca278552f62edf8ff7f8ebc6910ad9f0f391430c251b8538a7bb66

Aliases

arxiv: math/0408287 · arxiv_version: math/0408287v2 · doi: 10.48550/arxiv.math/0408287 · pith_short_12: HFAZY5HSZITY · pith_short_16: HFAZY5HSZITYKUXW · pith_short_8: HFAZY5HS

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/HFAZY5HSZITYKUXWF3PY757Y5P \
  | 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: 39419c74f2ca278552f62edf8ff7f8ebc6910ad9f0f391430c251b8538a7bb66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6246112213ca1c79ba0a11e091f49b8966b001028ffd499d627ab15e3f99168",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2004-08-20T23:12:46Z",
    "title_canon_sha256": "1abf9bdf28226f06b4c9c89b70730ad347b5b3acf8e2df0fc8c7b069d25b0a2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0408287",
    "kind": "arxiv",
    "version": 2
  }
}