Pith Number

pith:ME3RVPRA

pith:2025:ME3RVPRALTOCMA6AZ3TBX6MFIK

not attested not anchored not stored refs pending

Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations

Difeng Cai, Paulina Sep\'ulveda

arxiv:2506.23344 v1 · 2025-06-29 · math.NA · cs.LG · cs.NA · stat.ML

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ME3RVPRALTOCMA6AZ3TBX6MFIK}

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	2026-07-05T11:29:20.177189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61371abe205cdc2603c0cee61bf9854283121df2e9650f1456bcb8ec1091b5d8

Aliases

arxiv: 2506.23344 · arxiv_version: 2506.23344v1 · doi: 10.48550/arxiv.2506.23344 · pith_short_12: ME3RVPRALTOC · pith_short_16: ME3RVPRALTOCMA6A · pith_short_8: ME3RVPRA

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/ME3RVPRALTOCMA6AZ3TBX6MFIK \
  | 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: 61371abe205cdc2603c0cee61bf9854283121df2e9650f1456bcb8ec1091b5d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bce450532c02ea245619807c47f5d41ef8339fa82ca5b776741549d8836a50f3",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-06-29T17:39:41Z",
    "title_canon_sha256": "688b9dbfcb39604fedc3d8e7c7c8affa49597bdc55490f7caa1efb26bf676cb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.23344",
    "kind": "arxiv",
    "version": 1
  }
}