Pith Number

pith:ZK7PJQ4P

pith:2017:ZK7PJQ4PXAXG4IQMINBB46CWKV

not attested not anchored not stored refs pending

The singular Hartree equation in fractional perturbed Sobolev spaces

Alessandro Michelangeli, Alessandro Olgiati, Raffaele Scandone

arxiv:1711.04418 v3 · 2017-11-13 · math.AP · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZK7PJQ4PXAXG4IQMINBB46CWKV}

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	2026-05-18T00:10:11.101676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768

Aliases

arxiv: 1711.04418 · arxiv_version: 1711.04418v3 · doi: 10.48550/arxiv.1711.04418 · pith_short_12: ZK7PJQ4PXAXG · pith_short_16: ZK7PJQ4PXAXG4IQM · pith_short_8: ZK7PJQ4P

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/ZK7PJQ4PXAXG4IQMINBB46CWKV \
  | 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: cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afcb9d62b93d25f5fffed893719adaf9e78bef55566c999ec53627a1b9a4a355",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-11-13T04:23:50Z",
    "title_canon_sha256": "ac7254112b8198d0c3914f028dbba77e932cc2fd910336aa8567aa37fff39647"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.04418",
    "kind": "arxiv",
    "version": 3
  }
}