Pith Number

pith:6KFJI66W

pith:2020:6KFJI66WJB5OACYAV3RP3NSBYF

not attested not anchored not stored refs pending

Optimal Boltzmann hierarchies with non-vanishing spatial curvature

Cyril Pitrou, Julien Lesgourgues, Thiago S. Pereira

arxiv:2005.12119 v1 · 2020-05-25 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KFJI66WJB5OACYAV3RP3NSBYF}

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	2026-07-05T01:19:06.651459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f28a947bd6487ae00b00aee2fdb641c17860a1390285591fdaa4400dafe072cc

Aliases

arxiv: 2005.12119 · arxiv_version: 2005.12119v1 · doi: 10.48550/arxiv.2005.12119 · pith_short_12: 6KFJI66WJB5O · pith_short_16: 6KFJI66WJB5OACYA · pith_short_8: 6KFJI66W

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/6KFJI66WJB5OACYAV3RP3NSBYF \
  | 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: f28a947bd6487ae00b00aee2fdb641c17860a1390285591fdaa4400dafe072cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "559a1214fc8dd50736d3bae69f76848e3a0f0f3a9819416662b5d3afd7b89962",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2020-05-25T14:00:22Z",
    "title_canon_sha256": "558ffdbd337e12cd35f51db51eb985ff29abe0562ebdd8702b99d30c6d28345a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2005.12119",
    "kind": "arxiv",
    "version": 1
  }
}