Pith Number

pith:TGMQICUP

pith:2015:TGMQICUPMJSIIWKO2JYBCJCIEO

not attested not anchored not stored refs pending

The Cartan-Hadamard Theorem for Metric Spaces with Local Geodesic Bicombings

Benjamin Miesch

arxiv:1509.07001 v2 · 2015-09-23 · 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{TGMQICUPMJSIIWKO2JYBCJCIEO}

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	2026-05-18T01:00:10.086160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9999040a8f626484594ed270112448238d999895ae22fd2d3c893e40bc7814d6

Aliases

arxiv: 1509.07001 · arxiv_version: 1509.07001v2 · doi: 10.48550/arxiv.1509.07001 · pith_short_12: TGMQICUPMJSI · pith_short_16: TGMQICUPMJSIIWKO · pith_short_8: TGMQICUP

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/TGMQICUPMJSIIWKO2JYBCJCIEO \
  | 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: 9999040a8f626484594ed270112448238d999895ae22fd2d3c893e40bc7814d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87d082365f066c3d6c6f1e1c6766cacc296f74aaeaf2c1455fa02ad22d6d4373",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-09-23T14:18:39Z",
    "title_canon_sha256": "188c80621febc9ce2f2e50c5671ac6ec048ba91216b1202adfcfbf0f4e316575"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07001",
    "kind": "arxiv",
    "version": 2
  }
}