Pith Number

pith:IRDJLITF

pith:2018:IRDJLITF4Y7ZXURU7YPCBYQB4I

not attested not anchored not stored refs pending

Displacements of automorphisms of free groups I: Displacement functions, minpoints and train tracks

Armando Martino, Stefano Francaviglia

arxiv:1807.02781 v2 · 2018-07-08 · 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{IRDJLITF4Y7ZXURU7YPCBYQB4I}

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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

1 paper in Pith

The minimally displaced set of an irreducible automorphism is locally finite

Receipt and verification

First computed	2026-07-05T01:57:46.208790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

444695a265e63f9bd234fe1e20e201e220bfadcbb6485c6d92dd49eb01e7e60b

Aliases

arxiv: 1807.02781 · arxiv_version: 1807.02781v2 · doi: 10.48550/arxiv.1807.02781 · pith_short_12: IRDJLITF4Y7Z · pith_short_16: IRDJLITF4Y7ZXURU · pith_short_8: IRDJLITF

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/IRDJLITF4Y7ZXURU7YPCBYQB4I \
  | 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: 444695a265e63f9bd234fe1e20e201e220bfadcbb6485c6d92dd49eb01e7e60b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be893e2e557766fd3a519c2e6363808e00875b8818256c516c9733cbf4581203",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-07-08T08:44:40Z",
    "title_canon_sha256": "2229d69ab139a894da10c5d82138d25d9856a9d495b95d480d2bc451c0a4b9e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.02781",
    "kind": "arxiv",
    "version": 2
  }
}