Pith Number

pith:XJKI6MZV

pith:2014:XJKI6MZVZ2R2SMK4DV3TFLAATA

not attested not anchored not stored refs pending

A Morse Lemma for quasigeodesics in symmetric spaces and euclidean buildings

Bernhard Leeb, Joan Porti, Michael Kapovich

arxiv:1411.4176 v3 · 2014-11-15 · math.GR · math.DG · 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{XJKI6MZVZ2R2SMK4DV3TFLAATA}

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	2026-05-17T23:58:06.024740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba548f3335cea3a9315c1d7732ac00982ea505f5c5691da379e47cc73fe3eab1

Aliases

arxiv: 1411.4176 · arxiv_version: 1411.4176v3 · doi: 10.48550/arxiv.1411.4176 · pith_short_12: XJKI6MZVZ2R2 · pith_short_16: XJKI6MZVZ2R2SMK4 · pith_short_8: XJKI6MZV

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/XJKI6MZVZ2R2SMK4DV3TFLAATA \
  | 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: ba548f3335cea3a9315c1d7732ac00982ea505f5c5691da379e47cc73fe3eab1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69a6563a0b472d302b30d09d89a6f57aeabd008661a155f576781a4a205f2784",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-11-15T19:04:20Z",
    "title_canon_sha256": "57e2ddc2d63b82510ef7b473b0d3416f12a30481bbefc4ccf30d1648b2dfe4e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.4176",
    "kind": "arxiv",
    "version": 3
  }
}