Pith Number

pith:7NVBOICU

pith:2015:7NVBOICU64NXOTE33MFBDQUIVV

not attested not anchored not stored refs pending

Uncountable sets of unit vectors that are separated by more than 1

Tomasz Kania, Tomasz Kochanek

arxiv:1503.08166 v5 · 2015-03-27 · math.FA · 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{7NVBOICU64NXOTE33MFBDQUIVV}

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	2026-05-18T01:01:29.294777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb6a172054f71b774c9bdb0a11c288ad5fd828ccb07f6801642bc8c0acbaa870

Aliases

arxiv: 1503.08166 · arxiv_version: 1503.08166v5 · doi: 10.48550/arxiv.1503.08166 · pith_short_12: 7NVBOICU64NX · pith_short_16: 7NVBOICU64NXOTE3 · pith_short_8: 7NVBOICU

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/7NVBOICU64NXOTE33MFBDQUIVV \
  | 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: fb6a172054f71b774c9bdb0a11c288ad5fd828ccb07f6801642bc8c0acbaa870

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f090059a0ac91f96ecd5feaa5d28f175396385d0fe2d88b435412c1a7098473f",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-03-27T17:45:54Z",
    "title_canon_sha256": "2ed943242e3c7b0f7293c4df6db5a9025d3d30c7176b59b481d5c8206dd950e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08166",
    "kind": "arxiv",
    "version": 5
  }
}