Pith Number

pith:RGO5OO7E

pith:2015:RGO5OO7E2LZO7ZLQ3VPZY34SN2

not attested not anchored not stored refs pending

Long time behaviors for 3D cubic damped Klein-Gordon equations in inhomogeneous mediums

Lifeng Zhao, Ze Li

arxiv:1512.02755 v3 · 2015-12-09 · 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{RGO5OO7E2LZO7ZLQ3VPZY34SN2}

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	2026-05-18T00:54:48.046904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

899dd73be4d2f2efe570dd5f9c6f926e98ffb4923406b5dc1c4a58b2ca6a39bb

Aliases

arxiv: 1512.02755 · arxiv_version: 1512.02755v3 · doi: 10.48550/arxiv.1512.02755 · pith_short_12: RGO5OO7E2LZO · pith_short_16: RGO5OO7E2LZO7ZLQ · pith_short_8: RGO5OO7E

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/RGO5OO7E2LZO7ZLQ3VPZY34SN2 \
  | 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: 899dd73be4d2f2efe570dd5f9c6f926e98ffb4923406b5dc1c4a58b2ca6a39bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63c32ea0f525c6977eb6c094ed5e767bb2e462cb73c9fb34a60a769344fcf735",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-09T05:37:19Z",
    "title_canon_sha256": "419c31eac2aae687a4032e05df6b8c715513f9ff0c5f33413a44eb418bb88645"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02755",
    "kind": "arxiv",
    "version": 3
  }
}