Pith Number

pith:VSVALCPL

pith:2019:VSVALCPL75OGXV6O3Y7NACUUOP

not attested not anchored not stored refs pending

The Hartree-Fock equations in modulation spaces

Divyang G. Bhimani, Kasso A. Okoudjou, Manoussos Grillakis

arxiv:1908.05862 v1 · 2019-08-16 · 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{VSVALCPL75OGXV6O3Y7NACUUOP}

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	2026-07-04T23:57:53.850329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acaa0589ebff5c6bd7cede3ed00a9473dacc3417fd02a310ace3420ae0441044

Aliases

arxiv: 1908.05862 · arxiv_version: 1908.05862v1 · doi: 10.48550/arxiv.1908.05862 · pith_short_12: VSVALCPL75OG · pith_short_16: VSVALCPL75OGXV6O · pith_short_8: VSVALCPL

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/VSVALCPL75OGXV6O3Y7NACUUOP \
  | 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: acaa0589ebff5c6bd7cede3ed00a9473dacc3417fd02a310ace3420ae0441044

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c547b7fa4c41995029e2004691fd707ce2b2ee380698066de6a1926a393ee42f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-16T06:31:43Z",
    "title_canon_sha256": "dbdbf271cd476a3e62aafc6d5525228bc1b442696b23815a49e74463a5d6f82c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05862",
    "kind": "arxiv",
    "version": 1
  }
}