Pith Number

pith:R2ES4W5N

pith:2010:R2ES4W5NW37JYQ7XVR7KJBE6VF

not attested not anchored not stored refs pending

Homological stability for mapping class groups of surfaces

Nathalie Wahl

arxiv:1006.4476 v2 · 2010-06-23 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R2ES4W5NW37JYQ7XVR7KJBE6VF}

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	2026-05-18T03:37:09.399987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e892e5badb6fe9c43f7ac7ea4849ea9444a0f2a63a82a908f0f934e07d8b9dd

Aliases

arxiv: 1006.4476 · arxiv_version: 1006.4476v2 · doi: 10.48550/arxiv.1006.4476 · pith_short_12: R2ES4W5NW37J · pith_short_16: R2ES4W5NW37JYQ7X · pith_short_8: R2ES4W5N

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/R2ES4W5NW37JYQ7XVR7KJBE6VF \
  | 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: 8e892e5badb6fe9c43f7ac7ea4849ea9444a0f2a63a82a908f0f934e07d8b9dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29334761214eebea82822049613e25a0e4d7c587b37f9cb8887499db1960f009",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-06-23T11:30:58Z",
    "title_canon_sha256": "e707983d6e470ef84528de4b833f8973fc473274fcb7edd46538a85d5a05a6ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4476",
    "kind": "arxiv",
    "version": 2
  }
}