Pith Number

pith:LZFGOBJZ

pith:2025:LZFGOBJZ4B56OYD2UCLPKZ4JUH

not attested not anchored not stored refs pending

Non-affine Families of 8 x 8 Complex Hadamard Matrices

Tuomo Valtonen

arxiv:2505.22947 v2 · 2025-05-29 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LZFGOBJZ4B56OYD2UCLPKZ4JUH}

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	2026-07-05T11:26:31.652616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e4a670539e07be7607aa096f56789a1e6bfa534b7c23808957a0b5e90a5e54a

Aliases

arxiv: 2505.22947 · arxiv_version: 2505.22947v2 · doi: 10.48550/arxiv.2505.22947 · pith_short_12: LZFGOBJZ4B56 · pith_short_16: LZFGOBJZ4B56OYD2 · pith_short_8: LZFGOBJZ

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/LZFGOBJZ4B56OYD2UCLPKZ4JUH \
  | 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: 5e4a670539e07be7607aa096f56789a1e6bfa534b7c23808957a0b5e90a5e54a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8b2018970c6b9eeef4728260c6c51d1c1b2bfabee77515d196888fba2db0452",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-29T00:00:06Z",
    "title_canon_sha256": "a9e90c0d828be020784ecb67cc918468226b3af335599502b1ce4d6a3d101b66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.22947",
    "kind": "arxiv",
    "version": 2
  }
}