Pith Number

pith:CQ7QWINP

pith:2026:CQ7QWINPBMIRCUMXR5NKMWRSIC

not attested not anchored not stored refs pending

Solving Einstein's Vacuum Equations with Physics-Informed Neural Networks: Boundary Conditions and Domain Decomposition

Elly Bayona, Hernando Quevedo

arxiv:2608.08846 v1 · 2026-08-09 · 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{CQ7QWINPBMIRCUMXR5NKMWRSIC}

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	2026-08-11T01:25:31.214063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

143f0b21af0b111151978f5aa65a3240aab39f267d25f7b84ac73c91a14d1e92

Aliases

arxiv: 2608.08846 · arxiv_version: 2608.08846v1 · doi: 10.48550/arxiv.2608.08846 · pith_short_12: CQ7QWINPBMIR · pith_short_16: CQ7QWINPBMIRCUMX · pith_short_8: CQ7QWINP

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/CQ7QWINPBMIRCUMXR5NKMWRSIC \
  | 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: 143f0b21af0b111151978f5aa65a3240aab39f267d25f7b84ac73c91a14d1e92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b65571cba85287e64c431da4b19bfd66cdd46ea90cf4d686696e1b964e2e9e3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-08-09T18:16:17Z",
    "title_canon_sha256": "8ff930e8288fe25a986af52767a8f3803371323957f883e68ad9bf75b97956fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08846",
    "kind": "arxiv",
    "version": 1
  }
}