Pith Number

pith:OXZFT64W

pith:2012:OXZFT64WX4WCYX3XRZ3M6A5WKP

not attested not anchored not stored refs pending

Note on the Spectral Theorem

Daniel Williams, Tepper L Gill

arxiv:1211.0058 v1 · 2012-10-31 · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OXZFT64WX4WCYX3XRZ3M6A5WKP}

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	2026-05-18T03:41:43.246005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75f259fb96bf2c2c5f778e76cf03b653ec1f053feb4c9838df0569057243bfe5

Aliases

arxiv: 1211.0058 · arxiv_version: 1211.0058v1 · doi: 10.48550/arxiv.1211.0058 · pith_short_12: OXZFT64WX4WC · pith_short_16: OXZFT64WX4WCYX3X · pith_short_8: OXZFT64W

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/OXZFT64WX4WCYX3XRZ3M6A5WKP \
  | 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: 75f259fb96bf2c2c5f778e76cf03b653ec1f053feb4c9838df0569057243bfe5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "825b52f40044984d0c46ef7f2c5ca2979692ddd0740c1420534167c4c73d8e84",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-10-31T23:56:06Z",
    "title_canon_sha256": "908f2d038753915f9bbedd2c3a723d1186b9de65f3828d3022fe5c857d64c9c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0058",
    "kind": "arxiv",
    "version": 1
  }
}