Pith Number

pith:CRUXL3JA

pith:2018:CRUXL3JASM6DBZEER2RR5RBKXD

not attested not anchored not stored refs pending

Random outer automorphisms of free groups: Attracting trees and their singularity structures

Catherine Pfaff, Ilya Kapovich, Joseph Maher, Samuel J. Taylor

arxiv:1805.12382 v1 · 2018-05-31 · math.GR · 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{CRUXL3JASM6DBZEER2RR5RBKXD}

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	2026-05-18T00:14:30.399124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

146975ed20933c30e4848ea31ec42ab8c7ceb0453e3b6ce2d809176311adbc0a

Aliases

arxiv: 1805.12382 · arxiv_version: 1805.12382v1 · doi: 10.48550/arxiv.1805.12382 · pith_short_12: CRUXL3JASM6D · pith_short_16: CRUXL3JASM6DBZEE · pith_short_8: CRUXL3JA

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/CRUXL3JASM6DBZEER2RR5RBKXD \
  | 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: 146975ed20933c30e4848ea31ec42ab8c7ceb0453e3b6ce2d809176311adbc0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "592694f08679b4c62e3754042f6924a8af07a2ee4eb3f06c4e99e6109b96b50c",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-05-31T09:00:44Z",
    "title_canon_sha256": "fa1338dfb95beaacd2ca23c160046d0c8b5da21642ebdc364f18db44324efe09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.12382",
    "kind": "arxiv",
    "version": 1
  }
}