Pith Number

pith:D7AORPYM

pith:2011:D7AORPYMJOSCQ7UI5XWE6GD5LY

not attested not anchored not stored refs pending

Filling loops at infinity in the mapping class group

Aaron Abrams, Moon Duchin, Noel Brady, Pallavi Dani, Robert Young

arxiv:1109.6048 v2 · 2011-09-27 · 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{D7AORPYMJOSCQ7UI5XWE6GD5LY}

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	2026-05-18T03:56:33.979096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fc0e8bf0c4ba4287e88edec4f187d5e29ead40302658bb71eb17b93df96b692

Aliases

arxiv: 1109.6048 · arxiv_version: 1109.6048v2 · doi: 10.48550/arxiv.1109.6048 · pith_short_12: D7AORPYMJOSC · pith_short_16: D7AORPYMJOSCQ7UI · pith_short_8: D7AORPYM

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/D7AORPYMJOSCQ7UI5XWE6GD5LY \
  | 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: 1fc0e8bf0c4ba4287e88edec4f187d5e29ead40302658bb71eb17b93df96b692

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95c70dad8d24aaef9ceae65e27b9c18b0d0c50a62aaeab8da5e573eb281de50e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-09-27T21:48:51Z",
    "title_canon_sha256": "2de741c00b2358ba475219d7e103d9d9eff8955faf7130d09a561f19fdb25577"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6048",
    "kind": "arxiv",
    "version": 2
  }
}