Pith Number

pith:J4JVZLPH

pith:2012:J4JVZLPHUBIVDHHKXVKXHL33R3

not attested not anchored not stored refs pending

An explanation for galaxy rotation curves using a Clifford multivector spacetime framework

Azhar Iqbal, Derek Abbott, James M.Chappell, Nicolangelo Iannella

arxiv:1211.3507 v1 · 2012-11-15 · math-ph · gr-qc · 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{J4JVZLPHUBIVDHHKXVKXHL33R3}

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	2026-05-18T03:40:48.445854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f135cade7a051519ceabd5573af7b8ef64fbfe9305dcc85906808e1bb6cab85

Aliases

arxiv: 1211.3507 · arxiv_version: 1211.3507v1 · doi: 10.48550/arxiv.1211.3507 · pith_short_12: J4JVZLPHUBIV · pith_short_16: J4JVZLPHUBIVDHHK · pith_short_8: J4JVZLPH

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/J4JVZLPHUBIVDHHKXVKXHL33R3 \
  | 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: 4f135cade7a051519ceabd5573af7b8ef64fbfe9305dcc85906808e1bb6cab85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "534152b4725669ea1cb21e08f6afefb4f99ede2001d8f4c9866803ae730eae3b",
    "cross_cats_sorted": [
      "gr-qc",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-11-15T06:42:06Z",
    "title_canon_sha256": "be3771a16c6d1ef84ebff7c4c92968efef9f6774e6712bcc022c5a835c9ac176"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3507",
    "kind": "arxiv",
    "version": 1
  }
}