Pith Number

pith:HJ3KIPHH

pith:2025:HJ3KIPHHD35SCD7HPSCCNQXX5Y

not attested not anchored not stored refs pending

Effective Equation of State Oscillations at Matter-Radiation Equality and Primordial Gravitational Waves

S.D. Odintsov, V.K. Oikonomou

arxiv:2507.04571 v1 · 2025-07-06 · gr-qc · 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{HJ3KIPHHD35SCD7HPSCCNQXX5Y}

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	2026-07-05T11:32:49.926911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a76a43ce71efb210fe77c8426c2f7ee0647c56cc11ccee5c0891ef09195174d

Aliases

arxiv: 2507.04571 · arxiv_version: 2507.04571v1 · doi: 10.48550/arxiv.2507.04571 · pith_short_12: HJ3KIPHHD35S · pith_short_16: HJ3KIPHHD35SCD7H · pith_short_8: HJ3KIPHH

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/HJ3KIPHHD35SCD7HPSCCNQXX5Y \
  | 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: 3a76a43ce71efb210fe77c8426c2f7ee0647c56cc11ccee5c0891ef09195174d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3af420479c6050c86cd57677e4c13519b19e97bf65235c0021ace3a80c663be",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-07-06T22:59:36Z",
    "title_canon_sha256": "a714ffa2531b9b8982ba34fc3ecac850905f068bcf12395b67ebb4192546cba8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04571",
    "kind": "arxiv",
    "version": 1
  }
}