Pith Number

pith:P4JVHXXT

pith:2011:P4JVHXXTIXZQFXAUZZP5Z3WZ4P

not attested not anchored not stored refs pending

Closed Range for $\bar\partial$ and $\bar\partial_b$ on Bounded Hypersurfaces in Stein Manifolds

Andrew Raich, Phillip Harrington

arxiv:1106.0629 v1 · 2011-06-03 · math.CV · 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{P4JVHXXTIXZQFXAUZZP5Z3WZ4P}

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	2026-05-18T04:20:39.948591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f1353def345f302dc14ce5fdceed9e3ed1a05cf76dd2b0eb0348a7d6ab7178b

Aliases

arxiv: 1106.0629 · arxiv_version: 1106.0629v1 · doi: 10.48550/arxiv.1106.0629 · pith_short_12: P4JVHXXTIXZQ · pith_short_16: P4JVHXXTIXZQFXAU · pith_short_8: P4JVHXXT

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/P4JVHXXTIXZQFXAUZZP5Z3WZ4P \
  | 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: 7f1353def345f302dc14ce5fdceed9e3ed1a05cf76dd2b0eb0348a7d6ab7178b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "943cdfe82aa665cc81abe6681e7141080e44ec3b7ddb1617f988bce6fde34316",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-06-03T13:14:30Z",
    "title_canon_sha256": "771db357977ea196ec8925c43048e78a7e5430a134b25503d5a8282902920cf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0629",
    "kind": "arxiv",
    "version": 1
  }
}