Pith Number

pith:VXEHWFIP

pith:2012:VXEHWFIPLZQEU3B57BJY7XXKUO

not attested not anchored not stored refs pending

Geodesic Congruences and Their Deformations in Bertrand Space-times

Kaushik Bhattacharya, Prashant Kumar, Tapobrata Sarkar

arxiv:1206.4249 v2 · 2012-06-19 · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXEHWFIPLZQEU3B57BJY7XXKUO}

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	2026-05-18T01:56:50.869359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adc87b150f5e604a6c3df8538fdeeaa3ac8b3eeecd8956af48a174e43196d74e

Aliases

arxiv: 1206.4249 · arxiv_version: 1206.4249v2 · doi: 10.48550/arxiv.1206.4249 · pith_short_12: VXEHWFIPLZQE · pith_short_16: VXEHWFIPLZQEU3B5 · pith_short_8: VXEHWFIP

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/VXEHWFIPLZQEU3B57BJY7XXKUO \
  | 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: adc87b150f5e604a6c3df8538fdeeaa3ac8b3eeecd8956af48a174e43196d74e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db40a4ecfee22db4d8b7285730d49f3b3a143c103d5352e0ae50e44de83f89ac",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-06-19T15:57:52Z",
    "title_canon_sha256": "93f4d7d99cabc497146d0e0c7836479ff2076a5b13e0dd2a1c99187c99829d82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4249",
    "kind": "arxiv",
    "version": 2
  }
}