Pith Number

pith:GTHIPA4M

pith:2011:GTHIPA4M5MCHY4R4YUH3DSXH36

not attested not anchored not stored refs pending

Dynamics of Modified Chaplygin Gas in Brane World Scenario: Phase Plane Analysis

Prabir Rudra, Ritabrata Biswas, Ujjal Debnath

arxiv:1109.1481 v4 · 2011-09-07 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTHIPA4M5MCHY4R4YUH3DSXH36}

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	2026-05-18T04:00:28.359070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34ce87838ceb047c723cc50fb1cae7dfbb67958513d71e65e29ee8dd3bd30775

Aliases

arxiv: 1109.1481 · arxiv_version: 1109.1481v4 · doi: 10.48550/arxiv.1109.1481 · pith_short_12: GTHIPA4M5MCH · pith_short_16: GTHIPA4M5MCHY4R4 · pith_short_8: GTHIPA4M

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/GTHIPA4M5MCHY4R4YUH3DSXH36 \
  | 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: 34ce87838ceb047c723cc50fb1cae7dfbb67958513d71e65e29ee8dd3bd30775

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5086f5e595080739268cdc6879ace607f6b9dfe3d9edcb5edcbddd0de34823a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-09-07T15:05:42Z",
    "title_canon_sha256": "7b5b2d007fb2b9fd14e576d01e379248f034b950ea216eea07aaf5e0a7249e28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1481",
    "kind": "arxiv",
    "version": 4
  }
}