Pith Number

pith:MWY3NK2Z

pith:2002:MWY3NK2ZQQYQVRCKQKFZRGBTPC

not attested not anchored not stored refs pending

Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density

Akira Takamura, Hidekazu Yokomakura, Keiichi Kimura

arxiv:hep-ph/0205295 v4 · 2002-05-26 · 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{MWY3NK2ZQQYQVRCKQKFZRGBTPC}

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

Impact of matter effects on the unitarity test of lepton mixing

Receipt and verification

First computed	2026-07-04T16:34:12.669386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65b1b6ab5984310ac44a828b98983378933158ae55c5a6c8554fb4c8382b9f01

Aliases

arxiv: hep-ph/0205295 · arxiv_version: hep-ph/0205295v4 · doi: 10.48550/arxiv.hep-ph/0205295 · pith_short_12: MWY3NK2ZQQYQ · pith_short_16: MWY3NK2ZQQYQVRCK · pith_short_8: MWY3NK2Z

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/MWY3NK2ZQQYQVRCKQKFZRGBTPC \
  | 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: 65b1b6ab5984310ac44a828b98983378933158ae55c5a6c8554fb4c8382b9f01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05e7bd2e47cad8822086ba90246a0a9e9d3bc2b01fcda3674af328c86964bb91",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2002-05-26T15:05:24Z",
    "title_canon_sha256": "b2c01bc36c0a60cc4a653db1dc8e4c62f87b7f886172cf034e3f848afde88548"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0205295",
    "kind": "arxiv",
    "version": 4
  }
}