Pith Number

pith:Z2UFSC2G

pith:2025:Z2UFSC2G3SU67I7TXHMCWL36BY

not attested not anchored not stored refs pending

Maximal stretch and Lipschitz maps on Riemannian manifolds of negative curvature

Gerhard Knieper, Xian Dai

arxiv:2507.02617 v2 · 2025-07-03 · math.DG · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z2UFSC2G3SU67I7TXHMCWL36BY}

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	2026-05-27T02:05:04.031997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cea8590b46dca9efa3f3b9d82b2f7e0e251cc932d17f864ed8bf693f98e6680f

Aliases

arxiv: 2507.02617 · arxiv_version: 2507.02617v2 · doi: 10.48550/arxiv.2507.02617 · pith_short_12: Z2UFSC2G3SU6 · pith_short_16: Z2UFSC2G3SU67I7T · pith_short_8: Z2UFSC2G

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/Z2UFSC2G3SU67I7TXHMCWL36BY \
  | 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: cea8590b46dca9efa3f3b9d82b2f7e0e251cc932d17f864ed8bf693f98e6680f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e0c1f450b8f156c6a1018625c8c457855006a060ea7ed93c63a8513e681712d",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-03T13:44:22Z",
    "title_canon_sha256": "8c921b9b5f03e2ffc3d55f4f1c639e7146ac8568d8592ec75d70875e39a80367"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02617",
    "kind": "arxiv",
    "version": 2
  }
}