Pith Number

pith:GMAUQ4R5

pith:2004:GMAUQ4R57SDSGTREJIX2FKQ5AZ

not attested not anchored not stored refs pending

Operator synthesis II. Individual synthesis and linear operator equations

Lyudmila Turowska, Victor Shulman

arxiv:math/0401091 v2 · 2004-01-09 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GMAUQ4R57SDSGTREJIX2FKQ5AZ}

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	2026-05-18T01:05:26.661715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

330148723dfc87234e244a2fa2aa1d064a96a7cc50d7596e50b604f6af62bf8b

Aliases

arxiv: math/0401091 · arxiv_version: math/0401091v2 · doi: 10.48550/arxiv.math/0401091 · pith_short_12: GMAUQ4R57SDS · pith_short_16: GMAUQ4R57SDSGTRE · pith_short_8: GMAUQ4R5

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/GMAUQ4R57SDSGTREJIX2FKQ5AZ \
  | 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: 330148723dfc87234e244a2fa2aa1d064a96a7cc50d7596e50b604f6af62bf8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aec892d5447172f76f14d74f273ab52d7d222e852699b5ed6a99f5bdc1bb4600",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2004-01-09T14:59:12Z",
    "title_canon_sha256": "ec17fb073c4fbc67e3189213928c7b89f7d16597afdd381e089b1b0297fd0563"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401091",
    "kind": "arxiv",
    "version": 2
  }
}