Pith Number

pith:BZ4NCRIU

pith:2026:BZ4NCRIUOHBXTMQ2C4ZVW3RZN7

not attested not anchored not stored refs pending

Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks

Hao Ma, Hong-Bo Jin, Shuanglin Huang, Tailin Wu, Xuefeng Feng, Yu-Chen Zhou, Yue-Liang Wu, Zhi-Chao Zhao, Zhoujian Cao

arxiv:2607.06002 v1 · 2026-07-07 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BZ4NCRIUOHBXTMQ2C4ZVW3RZN7}

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	2026-07-08T01:18:52.906376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f

Aliases

arxiv: 2607.06002 · arxiv_version: 2607.06002v1 · doi: 10.48550/arxiv.2607.06002 · pith_short_12: BZ4NCRIUOHBX · pith_short_16: BZ4NCRIUOHBXTMQ2 · pith_short_8: BZ4NCRIU

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/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7 \
  | 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: 0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb0c841c359616a30cb5460fe34723a51e08897ea379dcfc029939d9c1ce8194",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-07T08:43:39Z",
    "title_canon_sha256": "d106b3d8716537972e3f367700607869294ae089c81529f5c31b70ee8b14277b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06002",
    "kind": "arxiv",
    "version": 1
  }
}