Pith Number

pith:6FAK3DZ4

pith:2017:6FAK3DZ4KZDJUDB6MT3G65RU4G

not attested not anchored not stored refs pending

The Caccioppoli Ultrafunctions

Carlo Romano Grisanti, Luigi Carlo Berselli, Vieri Benci

arxiv:1707.09265 v1 · 2017-07-27 · 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{6FAK3DZ4KZDJUDB6MT3G65RU4G}

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	2026-05-18T00:39:16.614534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f140ad8f3c56469a0c3e64f66f7634e1971284c98bd943fceeb876d16a1fb48b

Aliases

arxiv: 1707.09265 · arxiv_version: 1707.09265v1 · doi: 10.48550/arxiv.1707.09265 · pith_short_12: 6FAK3DZ4KZDJ · pith_short_16: 6FAK3DZ4KZDJUDB6 · pith_short_8: 6FAK3DZ4

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/6FAK3DZ4KZDJUDB6MT3G65RU4G \
  | 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: f140ad8f3c56469a0c3e64f66f7634e1971284c98bd943fceeb876d16a1fb48b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf8b8b35601cdb3ed934e69e60160195c58841cef75193ed0d847291bf5fa3a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-07-27T16:10:20Z",
    "title_canon_sha256": "5c4a81839b5caa9737126c6e82bb70f421c613f86f0641640f7a8631d5b427fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.09265",
    "kind": "arxiv",
    "version": 1
  }
}