Pith Number

pith:KYEE7RXJ

pith:2014:KYEE7RXJCPJXK7EWHQN2ITT7KE

not attested not anchored not stored refs pending

Lecture notes on thermodynamics of ideal string gases and its application in cosmology

Lihui Liu

arxiv:1412.2059 v1 · 2014-12-05 · 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{KYEE7RXJCPJXK7EWHQN2ITT7KE}

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	2026-05-18T02:32:05.473736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56084fc6e913d3757c963c1ba44e7f5102816e0171b059c7774401189a3646d2

Aliases

arxiv: 1412.2059 · arxiv_version: 1412.2059v1 · doi: 10.48550/arxiv.1412.2059 · pith_short_12: KYEE7RXJCPJX · pith_short_16: KYEE7RXJCPJXK7EW · pith_short_8: KYEE7RXJ

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/KYEE7RXJCPJXK7EWHQN2ITT7KE \
  | 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: 56084fc6e913d3757c963c1ba44e7f5102816e0171b059c7774401189a3646d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2fa93674856400f4623b47b519c1c1f4ce19b6787ecd2af9be619e31abd8045",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2014-12-05T16:50:05Z",
    "title_canon_sha256": "dae57067498d74755eb8040674437b35bfb1565eb9c3503cc631d7506f2659ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2059",
    "kind": "arxiv",
    "version": 1
  }
}