Pith Number

pith:Y3MU7BH6

pith:2025:Y3MU7BH6UYQU2LX5PAKAM6LW66

not attested not anchored not stored refs pending

Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems

Chunyan Li, Qi Wang, Wenkai Yu

arxiv:2507.09757 v1 · 2025-07-13 · math.NA · cs.LG · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y3MU7BH6UYQU2LX5PAKAM6LW66}

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	2026-07-05T11:36:39.258182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6d94f84fea6214d2efd7814067976f7bd5427b4c729d0b9d28b8569b8d41cab

Aliases

arxiv: 2507.09757 · arxiv_version: 2507.09757v1 · doi: 10.48550/arxiv.2507.09757 · pith_short_12: Y3MU7BH6UYQU · pith_short_16: Y3MU7BH6UYQU2LX5 · pith_short_8: Y3MU7BH6

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/Y3MU7BH6UYQU2LX5PAKAM6LW66 \
  | 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: c6d94f84fea6214d2efd7814067976f7bd5427b4c729d0b9d28b8569b8d41cab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d69ebf65bff411da971daedb8b81c15ffc8f0bf35cb4c7b0cb0845f054086cc",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-13T19:34:58Z",
    "title_canon_sha256": "507c81eb57e8b59c39a352343be3905335d57285519b9e6afdcb19e927982686"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09757",
    "kind": "arxiv",
    "version": 1
  }
}