Pith Number

pith:HZMQPSBJ

pith:2018:HZMQPSBJ6EW5LOQOT2IGHB6DKJ

not attested not anchored not stored refs pending

First-order expansions for eigenvalues and eigenfunctions in periodic homogenization

Jinping Zhuge

arxiv:1804.10739 v1 · 2018-04-28 · 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{HZMQPSBJ6EW5LOQOT2IGHB6DKJ}

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	2026-05-18T00:17:15.698251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e5907c829f12dd5ba0e9e906387c3525edfa49b13f878c04f98017c32284c51

Aliases

arxiv: 1804.10739 · arxiv_version: 1804.10739v1 · doi: 10.48550/arxiv.1804.10739 · pith_short_12: HZMQPSBJ6EW5 · pith_short_16: HZMQPSBJ6EW5LOQO · pith_short_8: HZMQPSBJ

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/HZMQPSBJ6EW5LOQOT2IGHB6DKJ \
  | 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: 3e5907c829f12dd5ba0e9e906387c3525edfa49b13f878c04f98017c32284c51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b7893345a90306ec71351ae6915380b98ac101ae6b65ce56e32b83a3503f4d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-04-28T04:32:26Z",
    "title_canon_sha256": "dc3f0bada351bf24597556f205ce52fa7936f9b8ef8b03442e8623c3b94e166e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.10739",
    "kind": "arxiv",
    "version": 1
  }
}