Pith Number

pith:2HGO7OYP

pith:2026:2HGO7OYPLGOXBQ6RNGFOHKHIJF

not attested not anchored not stored refs pending

Schauder-type Estimates and Log-Critical Well-posedness for the Two-Phase Muskat Problem with Surface Tension

Ke Chen, Quoc-Hung Nguyen, Ruilin Hu

arxiv:2606.12388 v1 · 2026-06-10 · 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{2HGO7OYPLGOXBQ6RNGFOHKHIJF}

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	2026-06-11T02:09:49.402105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1ccefbb0f599d70c3d1698ae3a8e84967819d174958e0ed4a1b6900cb0685a2

Aliases

arxiv: 2606.12388 · arxiv_version: 2606.12388v1 · doi: 10.48550/arxiv.2606.12388 · pith_short_12: 2HGO7OYPLGOX · pith_short_16: 2HGO7OYPLGOXBQ6R · pith_short_8: 2HGO7OYP

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/2HGO7OYPLGOXBQ6RNGFOHKHIJF \
  | 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: d1ccefbb0f599d70c3d1698ae3a8e84967819d174958e0ed4a1b6900cb0685a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "217c37582165269493343fb9c889672656d1a3d8c22037e3a2d16460d994b091",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-10T17:52:26Z",
    "title_canon_sha256": "18dc0624b4b7834cc2f6cc69426339d2804e4cacec3ba353895a353358e9c9ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12388",
    "kind": "arxiv",
    "version": 1
  }
}