Pith Number

pith:Z7L7OIRD

pith:2016:Z7L7OIRDVQN32FP4673YEXRCNB

not attested not anchored not stored refs pending

A Union of Euclidean Metric Spaces is Euclidean

Konstantin Makarychev, Yury Makarychev

arxiv:1602.08426 v3 · 2016-02-26 · 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{Z7L7OIRDVQN32FP4673YEXRCNB}

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	2026-05-18T00:52:17.507120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd7f72223ac1bbd15fcf7f7825e22684a48ad92556ec048ed965264a90f4337

Aliases

arxiv: 1602.08426 · arxiv_version: 1602.08426v3 · doi: 10.48550/arxiv.1602.08426 · pith_short_12: Z7L7OIRDVQN3 · pith_short_16: Z7L7OIRDVQN32FP4 · pith_short_8: Z7L7OIRD

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/Z7L7OIRDVQN32FP4673YEXRCNB \
  | 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: cfd7f72223ac1bbd15fcf7f7825e22684a48ad92556ec048ed965264a90f4337

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9b4b1d4750f1820dbb9a84c538a58a8206a1ddd67f0e8a1aa2345293857a5b7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-02-26T18:34:05Z",
    "title_canon_sha256": "ebc8631731acefc8d7522b74164277b20a685f7d9e65cb3c6fa4f0b312f1e309"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08426",
    "kind": "arxiv",
    "version": 3
  }
}