Pith Number

pith:O5CKCSBU

pith:2014:O5CKCSBU3UFCXYV4YT55VYM37Z

not attested not anchored not stored refs pending

Sharp $L^p$-bounds for the wave equation on groups of Heisenberg type

Andreas Seeger, Detlef M\"uller

arxiv:1408.3051 v1 · 2014-08-13 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O5CKCSBU3UFCXYV4YT55VYM37Z}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:22:21.886147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7744a14834dd0a2be2bcc4fbdae19bfe71cfeb4fa7c3b6ec17560fcc0556276a

Aliases

arxiv: 1408.3051 · arxiv_version: 1408.3051v1 · doi: 10.48550/arxiv.1408.3051 · pith_short_12: O5CKCSBU3UFC · pith_short_16: O5CKCSBU3UFCXYV4 · pith_short_8: O5CKCSBU

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/O5CKCSBU3UFCXYV4YT55VYM37Z \
  | 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: 7744a14834dd0a2be2bcc4fbdae19bfe71cfeb4fa7c3b6ec17560fcc0556276a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce9d51275fe3632d967b8550558c869c911fc8a4ed7029d3927c0468a29ba65c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-08-13T16:51:49Z",
    "title_canon_sha256": "93f29cdb5ff462d7d0adb3ac7f409f4cf21b589e1f2aa0e55ca838b6e85f4775"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.3051",
    "kind": "arxiv",
    "version": 1
  }
}