Pith Number

pith:TFJPVOCM

pith:2024:TFJPVOCMEJOJTA7H4PHUQFS3I3

not attested not anchored not stored refs pending

Harnack inequality for singular or degenerate parabolic equations in non-divergence form

Junyuan Fang, Sungwon Cho, Tuoc Phan

arxiv:2409.09437 v2 · 2024-09-14 · 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{TFJPVOCMEJOJTA7H4PHUQFS3I3}

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	2026-07-05T09:18:29.995669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9952fab84c225c9983e7e3cf48165b46da854f5564f1acee87379fd6cccb912f

Aliases

arxiv: 2409.09437 · arxiv_version: 2409.09437v2 · doi: 10.48550/arxiv.2409.09437 · pith_short_12: TFJPVOCMEJOJ · pith_short_16: TFJPVOCMEJOJTA7H · pith_short_8: TFJPVOCM

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/TFJPVOCMEJOJTA7H4PHUQFS3I3 \
  | 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: 9952fab84c225c9983e7e3cf48165b46da854f5564f1acee87379fd6cccb912f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36c6378cdf49f55145d1e82320fde4c224f75ab02fddbd9d4d3e34644dea4308",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-09-14T13:33:33Z",
    "title_canon_sha256": "52ee293e999c132d33619a3cae5b8f46828894f1cefa28166feae93da19bbeb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.09437",
    "kind": "arxiv",
    "version": 2
  }
}