Pith Number

pith:P4JJCMKE

pith:2016:P4JJCMKEDZWYNU6YL5JC7W3RZE

not attested not anchored not stored refs pending

Gradient Estimates via Rearrangements for Solutions of Some Schr\"odinger Equations

Dachun Yang, Der-Chen Chang, Sibei Yang, Zunwei Fu

arxiv:1603.00612 v1 · 2016-03-02 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4JJCMKEDZWYNU6YL5JC7W3RZE}

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	2026-05-18T01:19:43.340989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f129131441e6d86d3d85f522fdb71c915d0c65561c54e162d549c30e65c4955

Aliases

arxiv: 1603.00612 · arxiv_version: 1603.00612v1 · doi: 10.48550/arxiv.1603.00612 · pith_short_12: P4JJCMKEDZWY · pith_short_16: P4JJCMKEDZWYNU6Y · pith_short_8: P4JJCMKE

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/P4JJCMKEDZWYNU6YL5JC7W3RZE \
  | 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: 7f129131441e6d86d3d85f522fdb71c915d0c65561c54e162d549c30e65c4955

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "627b1ffdefe82b9b707a942737e8f02419fd1fa7557317d1382bea4b99804db6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-03-02T08:33:35Z",
    "title_canon_sha256": "0eca1c9e5c1af13f841670381cb5907af1740ce4b133179b74d2384788f17cab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00612",
    "kind": "arxiv",
    "version": 1
  }
}