Pith Number

pith:BHU3ZNLR

pith:2003:BHU3ZNLRJBOASZUNCPZ2AR3WZZ

not attested not anchored not stored refs pending

Magnus Expansion and Three-Neutrino Oscillations in Matter

Alexis A. Aguilar-Arevalo, J. C. D'Olivo, L. G. Cabral-Rosetti

arxiv:hep-ph/0302017 v3 · 2003-02-03 · 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{BHU3ZNLRJBOASZUNCPZ2AR3WZZ}

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	2026-07-04T16:40:29.398241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09e9bcb571485c09668d13f3a04776ce5763565563699e05e397bedeb3977857

Aliases

arxiv: hep-ph/0302017 · arxiv_version: hep-ph/0302017v3 · doi: 10.48550/arxiv.hep-ph/0302017 · pith_short_12: BHU3ZNLRJBOA · pith_short_16: BHU3ZNLRJBOASZUN · pith_short_8: BHU3ZNLR

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/BHU3ZNLRJBOASZUNCPZ2AR3WZZ \
  | 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: 09e9bcb571485c09668d13f3a04776ce5763565563699e05e397bedeb3977857

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21a81ffb458afc8ade3d9595118f2621da549c03aa881a1dc704f9ecd1c69dbb",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2003-02-03T23:08:03Z",
    "title_canon_sha256": "5d5388f28ab91aff513895b1cd47ef8bfcf5f9e135facf020a50d21f010fd8de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0302017",
    "kind": "arxiv",
    "version": 3
  }
}