Pith Number

pith:4QXQOCVS

pith:2015:4QXQOCVSQQ75D6C2P3DAHU5T7W

not attested not anchored not stored refs pending

Path algebras, wave-particle duality, and quantization of phase space

Murray Gerstenhaber

arxiv:1505.05859 v7 · 2015-05-21 · math.RA · math-ph · math.MP · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QXQOCVSQQ75D6C2P3DAHU5T7W}

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	2026-05-18T00:54:41.619424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e42f070ab2843fd1f85a7ec603d3b3fda3350ddd35fd18fb7c1b884c54173783

Aliases

arxiv: 1505.05859 · arxiv_version: 1505.05859v7 · doi: 10.48550/arxiv.1505.05859 · pith_short_12: 4QXQOCVSQQ75 · pith_short_16: 4QXQOCVSQQ75D6C2 · pith_short_8: 4QXQOCVS

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/4QXQOCVSQQ75D6C2P3DAHU5T7W \
  | 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: e42f070ab2843fd1f85a7ec603d3b3fda3350ddd35fd18fb7c1b884c54173783

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44dbbfbb0567ffb13886ca3463f1a189fde2bb46cc7c41acacc568d9e5bae38f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-05-21T19:51:49Z",
    "title_canon_sha256": "e1932f7b89a38d12ba775b9c0e2c72c759495a90fd044300e0676ab7ad583b5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05859",
    "kind": "arxiv",
    "version": 7
  }
}