Pith Number

pith:2W23AS2U

pith:2012:2W23AS2UK42ITRYFQ5S33HZOS3

not attested not anchored not stored refs pending

State Constrained Optimization with Partial Differential Equations via Generalized Gradients

Richard Barnard

arxiv:1207.5390 v2 · 2012-07-23 · math.OC · 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{2W23AS2UK42ITRYFQ5S33HZOS3}

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	2026-05-18T03:32:20.007893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5b5b04b54573489c7058765bd9f2e96f5f9ca195f9dd7ee7e9b51c309d513fd

Aliases

arxiv: 1207.5390 · arxiv_version: 1207.5390v2 · doi: 10.48550/arxiv.1207.5390 · pith_short_12: 2W23AS2UK42I · pith_short_16: 2W23AS2UK42ITRYF · pith_short_8: 2W23AS2U

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/2W23AS2UK42ITRYFQ5S33HZOS3 \
  | 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: d5b5b04b54573489c7058765bd9f2e96f5f9ca195f9dd7ee7e9b51c309d513fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdb0487ffc8fc75eea751594bf7c5170ea36b11ca90111a3cb56f9405bc42ee0",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-07-23T13:42:39Z",
    "title_canon_sha256": "9ffb9e07e01d8d12001bedfc77cfc91b40007744bc7e2ad9305967a1fbca34c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5390",
    "kind": "arxiv",
    "version": 2
  }
}