Pith Number

pith:OVLF5273

pith:2019:OVLF5273BFI73LW333ANFZVDA5

not attested not anchored not stored refs pending

Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations

Qing Liu, Xiaodan Zhou

arxiv:1907.01701 v1 · 2019-07-03 · 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{OVLF5273BFI73LW333ANFZVDA5}

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	2026-05-17T23:41:35.432429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75565eebfb0951fdaedbdec0d2e6a30750ce8b71ce3e0353d4a6f043ef3e0c4d

Aliases

arxiv: 1907.01701 · arxiv_version: 1907.01701v1 · doi: 10.48550/arxiv.1907.01701 · pith_short_12: OVLF5273BFI7 · pith_short_16: OVLF5273BFI73LW3 · pith_short_8: OVLF5273

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/OVLF5273BFI73LW333ANFZVDA5 \
  | 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: 75565eebfb0951fdaedbdec0d2e6a30750ce8b71ce3e0353d4a6f043ef3e0c4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0966867e6ac18bd0171816ba504d49e96ad56a486c33dbd82a0a5722f5dd54e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-07-03T01:57:59Z",
    "title_canon_sha256": "595042af8d8577326e9a24ed9b62e35c72845e87ee0dbb7c3f842994b102b9f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.01701",
    "kind": "arxiv",
    "version": 1
  }
}