Pith Number

pith:X4XIBUKA

pith:2013:X4XIBUKAPI6PCIC4NRVCDNXMAA

not attested not anchored not stored refs pending

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

Alexandru Krist\'aly, Andrea Calogero, Zolt\'an M. Balogh

arxiv:1305.5638 v3 · 2013-05-24 · 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{X4XIBUKAPI6PCIC4NRVCDNXMAA}

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	2026-05-18T01:20:56.287295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf2e80d1407a3cf1205c6c6a21b6ec0036444288e9fd049317b81c1229146f4a

Aliases

arxiv: 1305.5638 · arxiv_version: 1305.5638v3 · doi: 10.48550/arxiv.1305.5638 · pith_short_12: X4XIBUKAPI6P · pith_short_16: X4XIBUKAPI6PCIC4 · pith_short_8: X4XIBUKA

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/X4XIBUKAPI6PCIC4NRVCDNXMAA \
  | 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: bf2e80d1407a3cf1205c6c6a21b6ec0036444288e9fd049317b81c1229146f4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afbab647d5458e157f8f50814c1ad9629054f742a4bd552e17e312998ff3ce90",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-05-24T07:18:51Z",
    "title_canon_sha256": "47bb05514fc233d58d1da379d106a798ed7bb35c003cf80783058d7a9bb34f28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.5638",
    "kind": "arxiv",
    "version": 3
  }
}