Pith Number

pith:WSPARDF2

pith:2007:WSPARDF2U7WFZIM4X2JHHOV576

not attested not anchored not stored refs pending

Duality of Positive Currents and Plurisubharmonic Functions in Calibrated Geometry

F. Reese Harvey, H. Blaine Lawson Jr

arxiv:0710.3921 v3 · 2007-10-21 · math.DG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WSPARDF2U7WFZIM4X2JHHOV576}

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	2026-05-18T00:28:27.919879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b49e088cbaa7ec5ca19cbe9273babdffa6bea7dda5c45e47d7c5681959ba88f1

Aliases

arxiv: 0710.3921 · arxiv_version: 0710.3921v3 · doi: 10.48550/arxiv.0710.3921 · pith_short_12: WSPARDF2U7WF · pith_short_16: WSPARDF2U7WFZIM4 · pith_short_8: WSPARDF2

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/WSPARDF2U7WFZIM4X2JHHOV576 \
  | 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: b49e088cbaa7ec5ca19cbe9273babdffa6bea7dda5c45e47d7c5681959ba88f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b2bfd70acea8e71dab50eba7bebb9b8025676b388afb403a3ce4fc19075394e",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2007-10-21T10:42:26Z",
    "title_canon_sha256": "7121da4419de4cca6d1b2252791845392fa7881a2506ae8d244d13085832087d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.3921",
    "kind": "arxiv",
    "version": 3
  }
}