Pith Number

pith:QNLAT7JU

pith:2011:QNLAT7JU3GT3TRW4R7XW5DIRAE

not attested not anchored not stored refs pending

A combinatorial characterization of tight fusion frames

Edward Richmond, Kurt Luoto, Marcin Bownik

arxiv:1112.3060 v1 · 2011-12-13 · math.FA · 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{QNLAT7JU3GT3TRW4R7XW5DIRAE}

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	2026-05-18T01:55:34.331440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

835609fd34d9a7b9c6dc8fef6e8d11012a4f56a84aee6d9127c2708c5a53f521

Aliases

arxiv: 1112.3060 · arxiv_version: 1112.3060v1 · doi: 10.48550/arxiv.1112.3060 · pith_short_12: QNLAT7JU3GT3 · pith_short_16: QNLAT7JU3GT3TRW4 · pith_short_8: QNLAT7JU

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/QNLAT7JU3GT3TRW4R7XW5DIRAE \
  | 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: 835609fd34d9a7b9c6dc8fef6e8d11012a4f56a84aee6d9127c2708c5a53f521

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d87af1168ab8a9bfa31fdadf7aede194a4fe995ee59fadb38733c518a9bac069",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-12-13T22:19:17Z",
    "title_canon_sha256": "4fec49b2c0c387bd932d010dd7ea752630cd3b81b3026f280c6cdb8093bec5ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3060",
    "kind": "arxiv",
    "version": 1
  }
}