Pith Number

pith:PFPUDA4Y

pith:2010:PFPUDA4Y2U6ZYP3BWGRZXUNSC5

not attested not anchored not stored refs pending

On the geometry of a proposed curve complex analogue for $Out(F_n)$

Dmytro Savchuk, Lucas Sabalka

arxiv:1007.1998 v3 · 2010-07-12 · 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{PFPUDA4Y2U6ZYP3BWGRZXUNSC5}

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	2026-05-18T04:27:45.215248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

795f418398d53d9c3f61b1a39bd1b217561b0f172b726683fab45fda7ece58ab

Aliases

arxiv: 1007.1998 · arxiv_version: 1007.1998v3 · doi: 10.48550/arxiv.1007.1998 · pith_short_12: PFPUDA4Y2U6Z · pith_short_16: PFPUDA4Y2U6ZYP3B · pith_short_8: PFPUDA4Y

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/PFPUDA4Y2U6ZYP3BWGRZXUNSC5 \
  | 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: 795f418398d53d9c3f61b1a39bd1b217561b0f172b726683fab45fda7ece58ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1e3548f7444d7572cb5cefab5dd4ab84321f34ce3bfb750ac5727f247cf3aaa",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-07-12T21:37:30Z",
    "title_canon_sha256": "26b72c5cd09cdadcefb8e7368496976b6fffdee5260d9b66fd3653461eec1534"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1998",
    "kind": "arxiv",
    "version": 3
  }
}