Pith Number

pith:6NWD5WOT

pith:1999:6NWD5WOTGWNBWUNZ6SKGF3AC2B

not attested not anchored not stored refs pending

Bracket products for Weyl-Heisenberg frames

M. C. Lammers, Peter G. Casazza

arxiv:math/9911026 v1 · 1999-11-04 · 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{6NWD5WOTGWNBWUNZ6SKGF3AC2B}

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	2026-05-18T01:05:32.506622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f36c3ed9d3359a1b51b9f49462ec02d04a11e3dcd76d8eeb0459ac5e2675e458

Aliases

arxiv: math/9911026 · arxiv_version: math/9911026v1 · doi: 10.48550/arxiv.math/9911026 · pith_short_12: 6NWD5WOTGWNB · pith_short_16: 6NWD5WOTGWNBWUNZ · pith_short_8: 6NWD5WOT

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/6NWD5WOTGWNBWUNZ6SKGF3AC2B \
  | 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: f36c3ed9d3359a1b51b9f49462ec02d04a11e3dcd76d8eeb0459ac5e2675e458

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d465fca99d26b9db00c1acf8ea1dcbd02ea9a52cdbe967412deb18d2ad0aca9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "1999-11-04T18:06:06Z",
    "title_canon_sha256": "7d52f4f5d8f4319de375210c9cb8c374c45244752b4792847d508ccc010e0cf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911026",
    "kind": "arxiv",
    "version": 1
  }
}