Pith Number

pith:DY2NCNRK

pith:2017:DY2NCNRKROF72SQ7ELYHODPKVO

not attested not anchored not stored refs pending

A short proof of commutator estimates

Piero D'Ancona

arxiv:1709.01294 v3 · 2017-09-05 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DY2NCNRKROF72SQ7ELYHODPKVO}

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	2026-05-17T23:39:42.115502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e34d1362a8b8bfd4a1f22f0770deaabb2a2ec3b1b4fd4ed4ab08b7a0f1bb899

Aliases

arxiv: 1709.01294 · arxiv_version: 1709.01294v3 · doi: 10.48550/arxiv.1709.01294 · pith_short_12: DY2NCNRKROF7 · pith_short_16: DY2NCNRKROF72SQ7 · pith_short_8: DY2NCNRK

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/DY2NCNRKROF72SQ7ELYHODPKVO \
  | 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: 1e34d1362a8b8bfd4a1f22f0770deaabb2a2ec3b1b4fd4ed4ab08b7a0f1bb899

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c1aa13206c2638df0bf826f5e099dfa6f3a73f5c60243cfd07f722852307c86",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-09-05T09:08:09Z",
    "title_canon_sha256": "b2a22fb069a7a4011eac398b8bd13716e8709cdfd2b85be1e4a2486bf32d8a83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.01294",
    "kind": "arxiv",
    "version": 3
  }
}