Pith Number

pith:O4MNC35Q

pith:2016:O4MNC35QAFKNFWIU73WHLI4GTM

not attested not anchored not stored refs pending

Uniform rectifiability, elliptic measure, square functions, and $\varepsilon$-approximability via an ACF monotonicity formula

John Garnett, Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

arxiv:1612.02650 v3 · 2016-12-08 · math.CA · 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{O4MNC35QAFKNFWIU73WHLI4GTM}

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	2026-05-18T00:41:18.053768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167

Aliases

arxiv: 1612.02650 · arxiv_version: 1612.02650v3 · doi: 10.48550/arxiv.1612.02650 · pith_short_12: O4MNC35QAFKN · pith_short_16: O4MNC35QAFKNFWIU · pith_short_8: O4MNC35Q

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/O4MNC35QAFKNFWIU73WHLI4GTM \
  | 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: 7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c58dd8ce57d9476085011d9c211f3c5c363bcf2b7b0a5e84a627c68d7a1f7c0",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-12-08T14:11:43Z",
    "title_canon_sha256": "9fd27faada2db8c3c93a4b490eed570031bc009eb4c6ec950dbc063a98a0f5ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.02650",
    "kind": "arxiv",
    "version": 3
  }
}