Pith Number

pith:KF4XHU3W

pith:2003:KF4XHU3WZ2FMCXHO5ELCNZEWBA

not attested not anchored not stored refs pending

Lectures on the Theory of Cosmological Perturbations

Robert H. Brandenberger (Brown University)

arxiv:hep-th/0306071 v1 · 2003-06-09 · hep-th · astro-ph · gr-qc · hep-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KF4XHU3WZ2FMCXHO5ELCNZEWBA}

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

4 papers in Pith

On the Quantum-to-Classical Transition of Primordial Perturbations

Phase-resolved field-space distance bounds in ekpyrotic, bouncing and cyclic cosmologies

The Magnetic Origin of Primordial Black Holes: Ultralight PBHs and Secondary GWs

Phase-resolved field-space distance bounds in ekpyrotic, bouncing and cyclic cosmologies

Receipt and verification

First computed	2026-05-18T00:36:53.639415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

517973d376ce8ac15ceee91626e4960805e79f01d741ab72f69ec0a390713e89

Aliases

arxiv: hep-th/0306071 · arxiv_version: hep-th/0306071v1 · doi: 10.48550/arxiv.hep-th/0306071 · pith_short_12: KF4XHU3WZ2FM · pith_short_16: KF4XHU3WZ2FMCXHO · pith_short_8: KF4XHU3W

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/KF4XHU3WZ2FMCXHO5ELCNZEWBA \
  | 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: 517973d376ce8ac15ceee91626e4960805e79f01d741ab72f69ec0a390713e89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88609a4d6e31ad3134033905651bce396de7386fb087cf742dfa73594686d3b7",
    "cross_cats_sorted": [
      "astro-ph",
      "gr-qc",
      "hep-ph"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2003-06-09T14:35:13Z",
    "title_canon_sha256": "7f3f9dbe6db083c08c4bb5006cc7f796b7053c661079f240856a0f4667e60bfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0306071",
    "kind": "arxiv",
    "version": 1
  }
}