Pith Number

pith:CZHRJBWM

pith:2004:CZHRJBWM7AHFFKQSZZKVZDFF4H

not attested not anchored not stored refs pending

Linear Algebra for Mueller Calculus

A. Aiello, J. P. Woerdman

arxiv:math-ph/0412061 v3 · 2004-12-17 · math-ph · 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{CZHRJBWM7AHFFKQSZZKVZDFF4H}

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	2026-07-04T14:50:05.738881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

164f1486ccf80e52aa12ce555c8ca5e1c82d579bf06d8b253bd3e3ee42c1e7a9

Aliases

arxiv: math-ph/0412061 · arxiv_version: math-ph/0412061v3 · doi: 10.48550/arxiv.math-ph/0412061 · pith_short_12: CZHRJBWM7AHF · pith_short_16: CZHRJBWM7AHFFKQS · pith_short_8: CZHRJBWM

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/CZHRJBWM7AHFFKQSZZKVZDFF4H \
  | 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: 164f1486ccf80e52aa12ce555c8ca5e1c82d579bf06d8b253bd3e3ee42c1e7a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b11e1deadcdd32e24f365ccc9970aad1ea0231cc2153644acf013ea37eff265c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2004-12-17T07:50:13Z",
    "title_canon_sha256": "9935ed295fb6f8d9f64b79c7d5ed505e3a93773253680911e7604a7849ca76d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0412061",
    "kind": "arxiv",
    "version": 3
  }
}