Pith Number

pith:7MEZJUYG

pith:2013:7MEZJUYGHBZWZRVHCJNLRXC7X2

not attested not anchored not stored refs pending

A certain critical density property for invariant Harnack inequalities in H-type groups

Giulio Tralli

arxiv:1302.4999 v1 · 2013-02-20 · 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{7MEZJUYGHBZWZRVHCJNLRXC7X2}

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	2026-05-18T03:33:00.469836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb0994d30638736cc6a7125ab8dc5fbebd585c1d0a50e841b5ab240dde010f49

Aliases

arxiv: 1302.4999 · arxiv_version: 1302.4999v1 · doi: 10.48550/arxiv.1302.4999 · pith_short_12: 7MEZJUYGHBZW · pith_short_16: 7MEZJUYGHBZWZRVH · pith_short_8: 7MEZJUYG

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/7MEZJUYGHBZWZRVHCJNLRXC7X2 \
  | 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: fb0994d30638736cc6a7125ab8dc5fbebd585c1d0a50e841b5ab240dde010f49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f97ed34e4dcebe0807c17f9b471d2e25940fdc2a8036ba5664291d09b41e530",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-02-20T15:38:07Z",
    "title_canon_sha256": "53e6f56b8a632420afeaf1022304af2751ff5c6fe7473cbc5529680eadc11cfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4999",
    "kind": "arxiv",
    "version": 1
  }
}