Pith Number

pith:LKVAP54K

pith:2013:LKVAP54KNP46XNYX7UODFGZU42

not attested not anchored not stored refs pending

TASI Lectures on Cosmological Perturbations

Julien Lesgourgues

arxiv:1302.4640 v1 · 2013-02-19 · 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{LKVAP54KNP46XNYX7UODFGZU42}

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.

Cited by

1 paper in Pith

Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics

Receipt and verification

First computed	2026-05-18T03:33:12.577830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5aaa07f78a6bf9ebb717fd1c329b34e69ade883ccbfebf42ddc71eab191ecddd

Aliases

arxiv: 1302.4640 · arxiv_version: 1302.4640v1 · doi: 10.48550/arxiv.1302.4640 · pith_short_12: LKVAP54KNP46 · pith_short_16: LKVAP54KNP46XNYX · pith_short_8: LKVAP54K

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/LKVAP54KNP46XNYX7UODFGZU42 \
  | 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: 5aaa07f78a6bf9ebb717fd1c329b34e69ade883ccbfebf42ddc71eab191ecddd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b742f7d6bd91c0711701e7f49b509fec1c9121b7dfb9c84b4c419accaeddf68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-02-19T15:22:20Z",
    "title_canon_sha256": "aa8039ec7f0d45dd97a9d02a3bb2c6bfe11f0a4becbe2202abc06f1b11a32826"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4640",
    "kind": "arxiv",
    "version": 1
  }
}