Pith Number

pith:VXVYE76C

pith:2009:VXVYE76CKFD2DIRYS32BNDTXBI

not attested not anchored not stored refs pending

Cosmological Problems with Multiple Axion-like Fields

2), (2) Princeton University), Katherine J. Mack (1, Paul J. Steinhardt (2) ((1) IoA/KICC, University of Cambridge

arxiv:0911.0418 v1 · 2009-11-03 · astro-ph.CO · hep-ph · 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{VXVYE76CKFD2DIRYS32BNDTXBI}

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	2026-05-18T04:22:48.919679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adeb827fc25147a1a23896f4168e770a1032af1288ce6746dcce709816ab3675

Aliases

arxiv: 0911.0418 · arxiv_version: 0911.0418v1 · doi: 10.48550/arxiv.0911.0418 · pith_short_12: VXVYE76CKFD2 · pith_short_16: VXVYE76CKFD2DIRY · pith_short_8: VXVYE76C

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/VXVYE76CKFD2DIRYS32BNDTXBI \
  | 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: adeb827fc25147a1a23896f4168e770a1032af1288ce6746dcce709816ab3675

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abba5dc6bd6972455fdd62256ae745018241565f9b3093bd16e1aa9c244ff194",
    "cross_cats_sorted": [
      "hep-ph",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2009-11-03T10:46:20Z",
    "title_canon_sha256": "c9f30e86daafe24fdc82b05ea8c35b83620d594f572732f87f6265dcf2c56b91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.0418",
    "kind": "arxiv",
    "version": 1
  }
}