Pith Number

pith:52KFYTDT

pith:2022:52KFYTDTSHDWJNUDT3XSDMZY4B

not attested not anchored not stored refs pending

A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics

Jiaojiao Pan

arxiv:2211.07929 v1 · 2022-11-15 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{52KFYTDTSHDWJNUDT3XSDMZY4B}

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	2026-07-05T05:16:07.858746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6

Aliases

arxiv: 2211.07929 · arxiv_version: 2211.07929v1 · doi: 10.48550/arxiv.2211.07929 · pith_short_12: 52KFYTDTSHDW · pith_short_16: 52KFYTDTSHDWJNUD · pith_short_8: 52KFYTDT

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/52KFYTDTSHDWJNUDT3XSDMZY4B \
  | 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: ee945c4c7391c764b6839eef21b338e04995d47ee49a00bff87dd576f98632c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e1c9cfe0b94ea0fb5c133c7790f0b727316d79afc712b8743d1328233547caa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-11-15T06:25:16Z",
    "title_canon_sha256": "4623e9feeba0f7983b14a30928729478a0369eb70f514b604aec52c299a2f63c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.07929",
    "kind": "arxiv",
    "version": 1
  }
}