Pith Number

pith:LLPFP7KT

pith:2016:LLPFP7KTPS3ILZTP2MNSPX5RW4

not attested not anchored not stored refs pending

Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

Shun Zhou

arxiv:1612.03537 v2 · 2016-12-12 · hep-ph · hep-ex

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LLPFP7KTPS3ILZTP2MNSPX5RW4}

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	2026-05-18T00:49:36.338802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ade57fd537cb685e66fd31b27dfb1b70d3547c4124e371d997c8e49d60b7f24

Aliases

arxiv: 1612.03537 · arxiv_version: 1612.03537v2 · doi: 10.48550/arxiv.1612.03537 · pith_short_12: LLPFP7KTPS3I · pith_short_16: LLPFP7KTPS3ILZTP · pith_short_8: LLPFP7KT

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/LLPFP7KTPS3ILZTP2MNSPX5RW4 \
  | 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: 5ade57fd537cb685e66fd31b27dfb1b70d3547c4124e371d997c8e49d60b7f24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2e7dc291d8ae4707268f31773325a0506953ddbd3ea1c3e02e3f04331874dfe",
    "cross_cats_sorted": [
      "hep-ex"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2016-12-12T03:57:02Z",
    "title_canon_sha256": "28207071ef6e8593c24c6da8b3509598a37b515771814cd3f951da54f73ff1dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03537",
    "kind": "arxiv",
    "version": 2
  }
}