Pith Number

pith:GA2CAYBD

pith:2026:GA2CAYBDKXAYDR5WS3SZKOGFJN

not attested not anchored not stored refs pending

Inf-Sup Neural Networks for High Dimensional PDEs

Hailiang Liu, Ziren Chen

arxiv:2607.11718 v1 · 2026-07-13 · math.NA · cs.NA · 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{GA2CAYBDKXAYDR5WS3SZKOGFJN}

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	2026-07-14T02:22:20.627304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

303420602355c181c7b696e59538c54b54e3363ba243d4121dce8b8977353e72

Aliases

arxiv: 2607.11718 · arxiv_version: 2607.11718v1 · doi: 10.48550/arxiv.2607.11718 · pith_short_12: GA2CAYBDKXAY · pith_short_16: GA2CAYBDKXAYDR5W · pith_short_8: GA2CAYBD

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/GA2CAYBDKXAYDR5WS3SZKOGFJN \
  | 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: 303420602355c181c7b696e59538c54b54e3363ba243d4121dce8b8977353e72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87d1ea4334d419553d2f096910cdc04f686ac9f7d8af424da39ac5bf71aae728",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-13T15:44:08Z",
    "title_canon_sha256": "9959c9ca9a5844b22d8af0e1e54a5d5f2854ff8a795147f1f013e71fce78833d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11718",
    "kind": "arxiv",
    "version": 1
  }
}