Pith Number

pith:N2J3O2DL

pith:2013:N2J3O2DLGLGQNETOTR4UYC5WSK

not attested not anchored not stored refs pending

Unbounded Products of Operators and Connections to Dirac-Type Operators

Karl Gustafson, Mohammed Hichem Mortad

arxiv:1308.2427 v1 · 2013-08-11 · 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{N2J3O2DLGLGQNETOTR4UYC5WSK}

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	2026-05-18T03:04:08.263948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e93b7686b32cd06926e9c794c0bb6928cf116ce55e997e3358bdc21364389a6

Aliases

arxiv: 1308.2427 · arxiv_version: 1308.2427v1 · doi: 10.48550/arxiv.1308.2427 · pith_short_12: N2J3O2DLGLGQ · pith_short_16: N2J3O2DLGLGQNETO · pith_short_8: N2J3O2DL

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/N2J3O2DLGLGQNETOTR4UYC5WSK \
  | 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: 6e93b7686b32cd06926e9c794c0bb6928cf116ce55e997e3358bdc21364389a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b9d49d1479af1d6b2ef90cfdf1d1f0ef134280b9d17bda315d73feffb7b2fc7",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-08-11T20:22:48Z",
    "title_canon_sha256": "cc54a8e2b9bba9dfaed0ec9c090707968c4d329c912baa922685652e093e885d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2427",
    "kind": "arxiv",
    "version": 1
  }
}