Pith Number

pith:TYYZEH2L

pith:2026:TYYZEH2LE6QDE3JPNU2HCVUEJT

not attested not anchored not stored refs pending

Closed counterexamples to Toponogov's question on mixed curvature

Yaroslav Bazaikin

arxiv:2606.21610 v1 · 2026-06-19 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TYYZEH2LE6QDE3JPNU2HCVUEJT}

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	2026-06-23T01:13:16.207771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e31921f4b27a0326d2f6d347156844cd4358bd6e918e6084d7837802f1b527d

Aliases

arxiv: 2606.21610 · arxiv_version: 2606.21610v1 · doi: 10.48550/arxiv.2606.21610 · pith_short_12: TYYZEH2LE6QD · pith_short_16: TYYZEH2LE6QDE3JP · pith_short_8: TYYZEH2L

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/TYYZEH2LE6QDE3JPNU2HCVUEJT \
  | 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: 9e31921f4b27a0326d2f6d347156844cd4358bd6e918e6084d7837802f1b527d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f68e744e4cc9938ce5fb48f6c814cc8246c27dc6d538296a8aa6167a6eba1b4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-19T17:14:23Z",
    "title_canon_sha256": "7785f7c757b5a372cac4cb8e5be00c86723c22b1149aac97e12301f0449ad719"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21610",
    "kind": "arxiv",
    "version": 1
  }
}