Pith Number

pith:LP273VTN

pith:2015:LP273VTNKZMKS4TTTGGTT6RTKN

not attested not anchored not stored refs pending

Tukia's isomorphism theorem in CAT(-1) spaces

David Simmons, Mariusz Urba\'nski, Tushar Das

arxiv:1508.06960 v2 · 2015-08-27 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LP273VTNKZMKS4TTTGGTT6RTKN}

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	2026-05-18T00:00:13.848212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bf5fdd66d5658a97273998d39fa3353636891d7953591b4a7fedd5a15795815

Aliases

arxiv: 1508.06960 · arxiv_version: 1508.06960v2 · doi: 10.48550/arxiv.1508.06960 · pith_short_12: LP273VTNKZMK · pith_short_16: LP273VTNKZMKS4TT · pith_short_8: LP273VTN

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/LP273VTNKZMKS4TTTGGTT6RTKN \
  | 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: 5bf5fdd66d5658a97273998d39fa3353636891d7953591b4a7fedd5a15795815

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3402be992927cd195bba3dc002dd71793dc6286486aecce875a5588631344ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-08-27T18:20:51Z",
    "title_canon_sha256": "780b254cec8a439821485bc11137688b80365362899823c1d14852769ee531c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.06960",
    "kind": "arxiv",
    "version": 2
  }
}