Pith Number

pith:J45BBMIL

pith:2012:J45BBMIL6REGUEHTQR3D5EUDF6

not attested not anchored not stored refs pending

Para-Galilean versus Galilean Noncommutative Phase spaces

Ancille Ngendakumana, Joachim Nzotungicimpaye, Leonard Todjihounde

arxiv:1207.3919 v1 · 2012-07-17 · 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{J45BBMIL6REGUEHTQR3D5EUDF6}

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	2026-05-18T03:27:03.439222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f3a10b10bf4486a10f384763e92832f98887ccc126ec7642a552ae26bd9fc42

Aliases

arxiv: 1207.3919 · arxiv_version: 1207.3919v1 · doi: 10.48550/arxiv.1207.3919 · pith_short_12: J45BBMIL6REG · pith_short_16: J45BBMIL6REGUEHT · pith_short_8: J45BBMIL

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/J45BBMIL6REGUEHTQR3D5EUDF6 \
  | 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: 4f3a10b10bf4486a10f384763e92832f98887ccc126ec7642a552ae26bd9fc42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e03230ee5533fa6b9f163304f770ba3411e18386e752287d1d916a950346a57",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-07-17T08:59:45Z",
    "title_canon_sha256": "2b2a677b35b9f0787b480a2df144948926f375f0f583f1b6c759c3243b6f1e57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3919",
    "kind": "arxiv",
    "version": 1
  }
}