Pith Number

pith:ZUZ64TXS

pith:2015:ZUZ64TXSRRG6EDNY5OOG6ANBDM

not attested not anchored not stored refs pending

Proper curvature collineations in non-static plane symmetric space-times

Ghulam Shabbir, M. Ramzan

arxiv:1512.06957 v1 · 2015-12-22 · 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{ZUZ64TXSRRG6EDNY5OOG6ANBDM}

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	2026-05-18T01:23:53.337124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd33ee4ef28c4de20db8eb9c6f01a11b0592fbfe37a4d524418ce37c8bdaaa94

Aliases

arxiv: 1512.06957 · arxiv_version: 1512.06957v1 · doi: 10.48550/arxiv.1512.06957 · pith_short_12: ZUZ64TXSRRG6 · pith_short_16: ZUZ64TXSRRG6EDNY · pith_short_8: ZUZ64TXS

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/ZUZ64TXSRRG6EDNY5OOG6ANBDM \
  | 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: cd33ee4ef28c4de20db8eb9c6f01a11b0592fbfe37a4d524418ce37c8bdaaa94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e0ccc5b762ce8a726adee7667e0c3c51dfacc9620363f69f1d5c7b6fa9730c7",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-12-22T04:58:21Z",
    "title_canon_sha256": "cddf7cb2949866ba03b637e0810cab86170742294b122e922f192daba616210e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06957",
    "kind": "arxiv",
    "version": 1
  }
}