Pith Number

pith:A25HH4E3

pith:2016:A25HH4E3X4F4JNEFZGYXT7O2XE

not attested not anchored not stored refs pending

Polar Coordinates and Noncommutative Phase Space

August J. Krueger

arxiv:1610.07078 v1 · 2016-10-22 · 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{A25HH4E3X4F4JNEFZGYXT7O2XE}

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	2026-05-18T01:01:35.271846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06ba73f09bbf0bc4b485c9b179fddab919c46da9a1bf7d0f471d8000ba15b7b7

Aliases

arxiv: 1610.07078 · arxiv_version: 1610.07078v1 · doi: 10.48550/arxiv.1610.07078 · pith_short_12: A25HH4E3X4F4 · pith_short_16: A25HH4E3X4F4JNEF · pith_short_8: A25HH4E3

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/A25HH4E3X4F4JNEFZGYXT7O2XE \
  | 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: 06ba73f09bbf0bc4b485c9b179fddab919c46da9a1bf7d0f471d8000ba15b7b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d609e8a34cf653173865b681e26ce4f5b6b69c42018f6bce27f7506fb3ee3ca",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-10-22T17:19:56Z",
    "title_canon_sha256": "236e09376c2f44d529a409b640447a2b898b58c34c16a402e5e4d0406af7f7f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07078",
    "kind": "arxiv",
    "version": 1
  }
}