Pith Number

pith:C4VIMXWH

pith:2014:C4VIMXWHAT43CWRZJSCPOBLX27

not attested not anchored not stored refs pending

The Maximal Function and Square Function Control the Variation: An Elementary Proof

Bartosz Trojan, Ben Krause, Kevin Hughes

arxiv:1408.1213 v3 · 2014-08-06 · math.CA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C4VIMXWHAT43CWRZJSCPOBLX27}

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	2026-05-18T01:32:41.811892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

172a865ec704f9b15a394c84f70577d7c260f207697177c73eb511bb6f3e61b4

Aliases

arxiv: 1408.1213 · arxiv_version: 1408.1213v3 · doi: 10.48550/arxiv.1408.1213 · pith_short_12: C4VIMXWHAT43 · pith_short_16: C4VIMXWHAT43CWRZ · pith_short_8: C4VIMXWH

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/C4VIMXWHAT43CWRZJSCPOBLX27 \
  | 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: 172a865ec704f9b15a394c84f70577d7c260f207697177c73eb511bb6f3e61b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab98a62aa35e753db45594d6dd4f160a29a92944fce105ddb5d2ad441ea8c53d",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-08-06T08:45:48Z",
    "title_canon_sha256": "1482528c16db5f1a1650255acac204fb17ede29c52fca6e477d2bbc3f65037f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1213",
    "kind": "arxiv",
    "version": 3
  }
}