Pith Number

pith:PB5CDUTE

pith:2016:PB5CDUTEL5JWY7KFPX7CTJ6DEP

not attested not anchored not stored refs pending

The Aleksandrov-Bakelman-Pucci estimate and the Calabi-Yau equation

Ben Weinkove, Valentino Tosatti

arxiv:1607.02621 v1 · 2016-07-09 · math.DG · math.AP · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PB5CDUTEL5JWY7KFPX7CTJ6DEP}

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	2026-05-18T00:13:15.786547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

787a21d2645f536c7d457dfe29a7c323c2572cc36dc4f95ce21a203a183f5ee1

Aliases

arxiv: 1607.02621 · arxiv_version: 1607.02621v1 · doi: 10.48550/arxiv.1607.02621 · pith_short_12: PB5CDUTEL5JW · pith_short_16: PB5CDUTEL5JWY7KF · pith_short_8: PB5CDUTE

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/PB5CDUTEL5JWY7KFPX7CTJ6DEP \
  | 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: 787a21d2645f536c7d457dfe29a7c323c2572cc36dc4f95ce21a203a183f5ee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0372902debf23b7e3e161114f9418d02989e51fea6bf6ad2dc53af2b2265de3",
    "cross_cats_sorted": [
      "math.AP",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-07-09T15:04:47Z",
    "title_canon_sha256": "b827afc9d5d7dafcd43ab211db8b3f4ba531c2838f41be366f54aa1b00e1fb4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02621",
    "kind": "arxiv",
    "version": 1
  }
}