Pith Number

pith:J5LTKVBA

pith:2019:J5LTKVBACL62EH3SF67Y3PYGEC

not attested not anchored not stored refs pending

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds

Songbo Hou

arxiv:1908.03697 v1 · 2019-08-10 · math.DG · 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{J5LTKVBACL62EH3SF67Y3PYGEC}

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	2026-07-04T23:53:17.332520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f5735542012fda21f722fbf8dbf0620b497845ca618da9a1d5af0228e7c1ef4

Aliases

arxiv: 1908.03697 · arxiv_version: 1908.03697v1 · doi: 10.48550/arxiv.1908.03697 · pith_short_12: J5LTKVBACL62 · pith_short_16: J5LTKVBACL62EH3S · pith_short_8: J5LTKVBA

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/J5LTKVBACL62EH3SF67Y3PYGEC \
  | 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: 4f5735542012fda21f722fbf8dbf0620b497845ca618da9a1d5af0228e7c1ef4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ad7c1f68148d9f66c20878d3cd1cecc17920b1a0ac06d9ca7f78fa8414f9ca4",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-08-10T06:00:10Z",
    "title_canon_sha256": "b7cfde283bdb53b81d0389bb25c65df6d79cf3342836cc626f27e9427d8b679c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03697",
    "kind": "arxiv",
    "version": 1
  }
}