Pith Number

pith:PXXZBO5M

pith:2018:PXXZBO5M4KXC3NCXTXMRXS4FIW

not attested not anchored not stored refs pending

Boundary invariants and the closed range property for $\bar\partial$

Andrew Raich, Phillip S. Harrington

arxiv:1805.05793 v1 · 2018-05-15 · math.CV · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PXXZBO5M4KXC3NCXTXMRXS4FIW}

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	2026-05-18T00:15:53.677189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7def90bbace2ae2db4579dd91bcb85459aac1e2453c9dd3c7ee690029fb4cbd6

Aliases

arxiv: 1805.05793 · arxiv_version: 1805.05793v1 · doi: 10.48550/arxiv.1805.05793 · pith_short_12: PXXZBO5M4KXC · pith_short_16: PXXZBO5M4KXC3NCX · pith_short_8: PXXZBO5M

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/PXXZBO5M4KXC3NCXTXMRXS4FIW \
  | 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: 7def90bbace2ae2db4579dd91bcb85459aac1e2453c9dd3c7ee690029fb4cbd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02ab27a6329fc33606fc128f8b3f72ebf43ff8d6e268329bf16f3173cf1bfa05",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2018-05-15T14:17:16Z",
    "title_canon_sha256": "c36d0c4b9fdab8782aac744ac2ce3194dc9a1f21b69ced8c756b49fae44a8f7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.05793",
    "kind": "arxiv",
    "version": 1
  }
}