Pith Number

pith:IHQGZSE7

pith:2015:IHQGZSE7KBYZAQ66REZFOANRHH

not attested not anchored not stored refs pending

Cannon-Thurston maps for hyperbolic free group extensions

Ilya Kapovich, Samuel J. Taylor, Spencer Dowdall

arxiv:1506.06974 v3 · 2015-06-23 · 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{IHQGZSE7KBYZAQ66REZFOANRHH}

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	2026-05-18T01:24:24.732036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41e06cc89f50719043de89325701b139e19efb81897e3aa71ed5b4fcbd017a8a

Aliases

arxiv: 1506.06974 · arxiv_version: 1506.06974v3 · doi: 10.48550/arxiv.1506.06974 · pith_short_12: IHQGZSE7KBYZ · pith_short_16: IHQGZSE7KBYZAQ66 · pith_short_8: IHQGZSE7

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/IHQGZSE7KBYZAQ66REZFOANRHH \
  | 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: 41e06cc89f50719043de89325701b139e19efb81897e3aa71ed5b4fcbd017a8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3faf8dfa5c5c5f17371133bf5d0e3743f85187e4e17871c2c7d1d489a391c36c",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-23T12:51:18Z",
    "title_canon_sha256": "98dc45d76ff7b8939a628dcd8af9643ce7ae17911305735a81386dbc383d8933"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06974",
    "kind": "arxiv",
    "version": 3
  }
}