Pith Number

pith:MGOIZM47

pith:2021:MGOIZM47EHUGEMD2EDXBFYSR34

not attested not anchored not stored refs pending

A global shadow lemma and logarithm law for geometrically finite Hilbert geometries

Giulio Tiozzo, Harrison Bray

arxiv:2111.04618 v4 · 2021-11-08 · 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{MGOIZM47EHUGEMD2EDXBFYSR34}

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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.

Cited by

2 papers in Pith

A global shadow lemma for relatively Morse groups in higher rank

Simple-stable representations of surface groups in $\mathrm{PU}(2,1)$

Receipt and verification

First computed	2026-07-05T10:39:12.803968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

619c8cb39f21e862307a20ee12e251df1e4f848dda17b3a3084f050873266603

Aliases

arxiv: 2111.04618 · arxiv_version: 2111.04618v4 · doi: 10.48550/arxiv.2111.04618 · pith_short_12: MGOIZM47EHUG · pith_short_16: MGOIZM47EHUGEMD2 · pith_short_8: MGOIZM47

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/MGOIZM47EHUGEMD2EDXBFYSR34 \
  | 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: 619c8cb39f21e862307a20ee12e251df1e4f848dda17b3a3084f050873266603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a7ae89e99ddce0919312a9141b47f2297518b184c5c85c2a91869caa07f094f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-11-08T16:45:15Z",
    "title_canon_sha256": "d280e8a7834514bfe945a9fe0b9f85d7e0c11839df1224bf86160e44b0424760"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.04618",
    "kind": "arxiv",
    "version": 4
  }
}