Pith Number

pith:GUN46VVE

pith:2019:GUN46VVEFOKB3VXOLTXVS2JRTX

not attested not anchored not stored refs pending

Gradient estimates for divergence form elliptic systems arising from composite material

Hongjie Dong, Longjuan Xu

arxiv:1903.09914 v1 · 2019-03-24 · 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{GUN46VVEFOKB3VXOLTXVS2JRTX}

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	2026-05-17T23:50:35.097589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

351bcf56a42b941dd6ee5cef5969319ddf27f9580fb660a8153ba97f800d0a75

Aliases

arxiv: 1903.09914 · arxiv_version: 1903.09914v1 · doi: 10.48550/arxiv.1903.09914 · pith_short_12: GUN46VVEFOKB · pith_short_16: GUN46VVEFOKB3VXO · pith_short_8: GUN46VVE

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/GUN46VVEFOKB3VXOLTXVS2JRTX \
  | 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: 351bcf56a42b941dd6ee5cef5969319ddf27f9580fb660a8153ba97f800d0a75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd5211b82d871b02dceee136be0bd1380999763254032cccfd0dd936a63fac36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-03-24T02:45:29Z",
    "title_canon_sha256": "af43bb26b7d6148fe7df8d670a52e039e1e10faa219507da0c54042ec09cf9d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.09914",
    "kind": "arxiv",
    "version": 1
  }
}