Pith Number

pith:HR6FZIT2

pith:2026:HR6FZIT2FWXNNCCPNDCHRRNISZ

not attested not anchored not stored refs pending

Uniform Sobolev inequalities on geometric graphs

Samuel Mercer, Yves van Gennip

arxiv:2607.16948 v1 · 2026-07-18 · math.AP · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HR6FZIT2FWXNNCCPNDCHRRNISZ}

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	2026-07-21T01:21:07.747213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c7c5ca27a2daed6884f68c478c5a8966c05fd3afc23e6752af57cdca0b8d2e7

Aliases

arxiv: 2607.16948 · arxiv_version: 2607.16948v1 · doi: 10.48550/arxiv.2607.16948 · pith_short_12: HR6FZIT2FWXN · pith_short_16: HR6FZIT2FWXNNCCP · pith_short_8: HR6FZIT2

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/HR6FZIT2FWXNNCCPNDCHRRNISZ \
  | 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: 3c7c5ca27a2daed6884f68c478c5a8966c05fd3afc23e6752af57cdca0b8d2e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64f3bd3add7ff41d510c8d110b1751001cf3530c11b4c562b864074a19fb9abf",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-18T20:04:14Z",
    "title_canon_sha256": "fd6e3a6dc472b1118b31a51af8b53d3c0654f3ee6e74ac7a7036eb3859d1a735"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16948",
    "kind": "arxiv",
    "version": 1
  }
}