Pith Number

pith:5YCAUMIM

pith:2015:5YCAUMIM2TLUKT5X55OFMWU7E4

not attested not anchored not stored refs pending

Convergence Rates in Periodic Homogenization of Systems of Elasticity

Jinping Zhuge, Zhongwei Shen

arxiv:1512.00823 v1 · 2015-12-02 · 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{5YCAUMIM2TLUKT5X55OFMWU7E4}

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	2026-05-18T00:50:57.581583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512

Aliases

arxiv: 1512.00823 · arxiv_version: 1512.00823v1 · doi: 10.48550/arxiv.1512.00823 · pith_short_12: 5YCAUMIM2TLU · pith_short_16: 5YCAUMIM2TLUKT5X · pith_short_8: 5YCAUMIM

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/5YCAUMIM2TLUKT5X55OFMWU7E4 \
  | 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: ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23c35800c0d097ac014f97a27a776c0303a42a9799840985f8fcf8f6c71a797f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-02T19:55:33Z",
    "title_canon_sha256": "98c8c9156e26e345a2231a6401eec5bed9e59e72c17feddf2a2b867e68952ff1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00823",
    "kind": "arxiv",
    "version": 1
  }
}