Pith Number

pith:L3NPNQJU

pith:2018:L3NPNQJUX432EAIUXIJV2SPS6H

not attested not anchored not stored refs pending

Hyperbolic Immersions of Free Groups

Jean Pierre Mutanguha

arxiv:1809.04761 v2 · 2018-09-13 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L3NPNQJUX432EAIUXIJV2SPS6H}

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.

Cited by

1 paper in Pith

Irreducible Nonsurjective Endomorphisms of $F_n$ are Hyperbolic

Receipt and verification

First computed	2026-07-05T03:18:37.258074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5edaf6c134bf37a20114ba135d49f2f1c09fda3e2db9aa30e324901a8ad3a4da

Aliases

arxiv: 1809.04761 · arxiv_version: 1809.04761v2 · doi: 10.48550/arxiv.1809.04761 · pith_short_12: L3NPNQJUX432 · pith_short_16: L3NPNQJUX432EAIU · pith_short_8: L3NPNQJU

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/L3NPNQJUX432EAIUXIJV2SPS6H \
  | 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: 5edaf6c134bf37a20114ba135d49f2f1c09fda3e2db9aa30e324901a8ad3a4da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9fb420f4f78887afa0729e59987fc72d71fa0f15201b186a3a1669880e74577",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-09-13T04:01:48Z",
    "title_canon_sha256": "843d56044509cd77cf1b82c6bdf61fc2146db61d11fa3eaad4d1058d13eef1e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.04761",
    "kind": "arxiv",
    "version": 2
  }
}