Pith Number

pith:S4J76A4W

pith:2014:S4J76A4WOMPSBO3ABYZYIKQKUC

not attested not anchored not stored refs pending

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

Daniel Alpay, David P. Kimsey, Fabrizio Colombo

arxiv:1409.7010 v2 · 2014-09-24 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S4J76A4WOMPSBO3ABYZYIKQKUC}

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	2026-05-18T02:31:03.744446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9713ff0396731f20bb600e33842a0aa08546af116bd072d848fe089fd5ef75bf

Aliases

arxiv: 1409.7010 · arxiv_version: 1409.7010v2 · doi: 10.48550/arxiv.1409.7010 · pith_short_12: S4J76A4WOMPS · pith_short_16: S4J76A4WOMPSBO3A · pith_short_8: S4J76A4W

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/S4J76A4WOMPSBO3ABYZYIKQKUC \
  | 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: 9713ff0396731f20bb600e33842a0aa08546af116bd072d848fe089fd5ef75bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "033a5a2dfe6376490b85131550a78a0a45eab8a0e07cb478e9af66f1b0d0ca4d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2014-09-24T16:19:48Z",
    "title_canon_sha256": "9a6c85cf2e266dbeee03cb6bad99bf7057adfd3c9efbb4516abda4ddd2410d0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7010",
    "kind": "arxiv",
    "version": 2
  }
}