Pith Number

pith:IGFPJQXD

pith:2015:IGFPJQXDVQS57CQNYONCC7MZOT

not attested not anchored not stored refs pending

Tangent lines and Lipschitz differentiability spaces

Fabio Cavalletti, Tapio Rajala

arxiv:1503.01020 v2 · 2015-03-03 · math.MG · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IGFPJQXDVQS57CQNYONCC7MZOT}

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	2026-05-18T02:17:33.093143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

418af4c2e3ac25df8a0dc39a217d9974cff03ea700b2265d3448b893ab9b0c07

Aliases

arxiv: 1503.01020 · arxiv_version: 1503.01020v2 · doi: 10.48550/arxiv.1503.01020 · pith_short_12: IGFPJQXDVQS5 · pith_short_16: IGFPJQXDVQS57CQN · pith_short_8: IGFPJQXD

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/IGFPJQXDVQS57CQNYONCC7MZOT \
  | 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: 418af4c2e3ac25df8a0dc39a217d9974cff03ea700b2265d3448b893ab9b0c07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18056444c1655223f179b047e0fc99b23d1bf6a9483b01e2a69b119428ebc343",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-03-03T17:29:40Z",
    "title_canon_sha256": "daa52716d8c3b81757240a3473d8561e1d95d31d5e12883cac9b8969fbc12a7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.01020",
    "kind": "arxiv",
    "version": 2
  }
}