Pith Number

pith:6NIAUAEX

pith:2015:6NIAUAEXUUZENFNGAXQAP2KRR3

not attested not anchored not stored refs pending

A dense geodesic ray in the $Out(F_r)$-quotient of reduced Outer Space

Catherine Pfaff, Yael Algom-Kfir

arxiv:1508.05622 v3 · 2015-08-23 · math.GR · math.DS · 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{6NIAUAEXUUZENFNGAXQAP2KRR3}

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	2026-05-18T01:12:55.334501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3500a0097a5324695a605e007e9518eeaab0da2895ac63d42b3e641d6029a73

Aliases

arxiv: 1508.05622 · arxiv_version: 1508.05622v3 · doi: 10.48550/arxiv.1508.05622 · pith_short_12: 6NIAUAEXUUZE · pith_short_16: 6NIAUAEXUUZENFNG · pith_short_8: 6NIAUAEX

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/6NIAUAEXUUZENFNGAXQAP2KRR3 \
  | 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: f3500a0097a5324695a605e007e9518eeaab0da2895ac63d42b3e641d6029a73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b5b9da17deffb5ca1317127eb412e8b77169b3ba60f0280744f656091df91d0",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-08-23T15:40:58Z",
    "title_canon_sha256": "46611ba414a734e69fa1530cee4400687a273ad8a5366bc21983f4949be7fafb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05622",
    "kind": "arxiv",
    "version": 3
  }
}