Pith Number

pith:CQFHR4QC

pith:2000:CQFHR4QC65JHL2WLEJQZQUUFEM

not attested not anchored not stored refs pending

Classifying characteristic functions giving Weyl-Heisenberg frames

M.C. Lammers, P.G. Casazza

arxiv:math/0008175 v1 · 2000-08-22 · 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{CQFHR4QC65JHL2WLEJQZQUUFEM}

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	2026-05-18T01:38:30.181483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

140a78f202f75275eacb22619852852306da702e72fdd0830eb785a0de028aa0

Aliases

arxiv: math/0008175 · arxiv_version: math/0008175v1 · doi: 10.48550/arxiv.math/0008175 · pith_short_12: CQFHR4QC65JH · pith_short_16: CQFHR4QC65JHL2WL · pith_short_8: CQFHR4QC

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/CQFHR4QC65JHL2WLEJQZQUUFEM \
  | 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: 140a78f202f75275eacb22619852852306da702e72fdd0830eb785a0de028aa0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ce33af5a90f41996aaf7736b0df35d1dbc503dc70a7946e1cfd0abcddae5d2c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2000-08-22T19:16:58Z",
    "title_canon_sha256": "48ae4f12ef12b970d83721ce76cdd4fe7604e28e663510345249f07ca41a96d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0008175",
    "kind": "arxiv",
    "version": 1
  }
}