Pith Number

pith:YN6UA7QR

pith:2019:YN6UA7QRDWINCW5R3RSUXMCQSZ

not attested not anchored not stored refs pending

The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders

Bingyuan Liu, Phillip Harrington

arxiv:1905.04238 v1 · 2019-05-10 · 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{YN6UA7QRDWINCW5R3RSUXMCQSZ}

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	2026-05-17T23:46:31.656995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c37d407e111d90d15bb1dc654bb0509643188c8b5ec4461bab043cf7287d0258

Aliases

arxiv: 1905.04238 · arxiv_version: 1905.04238v1 · doi: 10.48550/arxiv.1905.04238 · pith_short_12: YN6UA7QRDWIN · pith_short_16: YN6UA7QRDWINCW5R · pith_short_8: YN6UA7QR

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/YN6UA7QRDWINCW5R3RSUXMCQSZ \
  | 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: c37d407e111d90d15bb1dc654bb0509643188c8b5ec4461bab043cf7287d0258

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff5f5cf2e0a1e565f210902e16fa0fb9ba23593bfca3e1a88895968cc03f118b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2019-05-10T16:12:47Z",
    "title_canon_sha256": "feedc5a26a4ffb09ce18f0bf955b3f370985c710e0d69c722d88e8889c5700a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.04238",
    "kind": "arxiv",
    "version": 1
  }
}