Pith Number

pith:PYZNBBML

pith:2015:PYZNBBML5SHBGGQMGYTJUB6MQZ

not attested not anchored not stored refs pending

Tangents, rectifiability, and corkscrew domains

Jonas Azzam

arxiv:1505.03960 v4 · 2015-05-15 · math.CA · math.AP · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PYZNBBML5SHBGGQMGYTJUB6MQZ}

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	2026-05-18T00:53:51.321356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e32d0858bec8e131a0c36269a07cc866126bfafd84ab1541a67cfcfa5b2b322

Aliases

arxiv: 1505.03960 · arxiv_version: 1505.03960v4 · doi: 10.48550/arxiv.1505.03960 · pith_short_12: PYZNBBML5SHB · pith_short_16: PYZNBBML5SHBGGQM · pith_short_8: PYZNBBML

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/PYZNBBML5SHBGGQMGYTJUB6MQZ \
  | 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: 7e32d0858bec8e131a0c36269a07cc866126bfafd84ab1541a67cfcfa5b2b322

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3809548c245559492de2d4c6a3550ea4ff155e12332eea95787e0c0c223808f",
    "cross_cats_sorted": [
      "math.AP",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-05-15T04:51:26Z",
    "title_canon_sha256": "f5e07260a9b7b1e5c3ac87240ca98983da0cc5025424a8fbe8c8abd6e0b87b7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.03960",
    "kind": "arxiv",
    "version": 4
  }
}