Pith Number

pith:ES5DX5EF

pith:2012:ES5DX5EFXR7KJ32HJ4SFHW3XQQ

not attested not anchored not stored refs pending

Solutions for Neumann boundary value problems involving $\big(p_{1}(x), p_{2}(x)\big)$-Laplace operators

Duchao Liu, Jinghua Yao, Xiaoyan Wang

arxiv:1205.3765 v1 · 2012-05-16 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ES5DX5EFXR7KJ32HJ4SFHW3XQQ}

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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	2026-05-18T03:55:25.228227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24ba3bf485bc7ea4ef474f2453db77840c50ccbe8a49666c9231a170178ff8f7

Aliases

arxiv: 1205.3765 · arxiv_version: 1205.3765v1 · doi: 10.48550/arxiv.1205.3765 · pith_short_12: ES5DX5EFXR7K · pith_short_16: ES5DX5EFXR7KJ32H · pith_short_8: ES5DX5EF

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/ES5DX5EFXR7KJ32HJ4SFHW3XQQ \
  | 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: 24ba3bf485bc7ea4ef474f2453db77840c50ccbe8a49666c9231a170178ff8f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cd1a521e7cdebb58cb52a0e960c92ed358896533778784c021aa377c9ccb56d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-05-16T19:10:53Z",
    "title_canon_sha256": "82c081d798e285c2120ad6e4784840a34bdab5ce33b2dc5acb99eb6502a3f11a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3765",
    "kind": "arxiv",
    "version": 1
  }
}