Pith Number

pith:TUVTKBC5

pith:2020:TUVTKBC5KGIOVSRYZSPJ2TBE44

not attested not anchored not stored refs pending

Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter

Shun Zhou

arxiv:2004.10570 v2 · 2020-04-22 · hep-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TUVTKBC5KGIOVSRYZSPJ2TBE44}

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	2026-07-05T03:46:12.257730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d2b35045d5190eaca38cc9e9d4c24e721d9af251fafa703016606a3af7d055b

Aliases

arxiv: 2004.10570 · arxiv_version: 2004.10570v2 · doi: 10.48550/arxiv.2004.10570 · pith_short_12: TUVTKBC5KGIO · pith_short_16: TUVTKBC5KGIOVSRY · pith_short_8: TUVTKBC5

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/TUVTKBC5KGIOVSRYZSPJ2TBE44 \
  | 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: 9d2b35045d5190eaca38cc9e9d4c24e721d9af251fafa703016606a3af7d055b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d548f64262547804eba7fbac3e2a871bec585c8d00b1292922263cbe614db318",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2020-04-22T13:45:48Z",
    "title_canon_sha256": "f87e3b9bbed5a12ff12da7e1292f8c3e71b7e5bd8f3f6120ecee92bce12c8cf4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.10570",
    "kind": "arxiv",
    "version": 2
  }
}