Pith Number

pith:ZJJRC7KX

pith:2025:ZJJRC7KXSOFJXS4XAIXJE7XUB6

not attested not anchored not stored refs pending

Surjectivity of the Cannon--Thurston map in metric (graph) bundles

Rakesh Halder

arxiv:2507.07076 v1 · 2025-07-09 · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZJJRC7KXSOFJXS4XAIXJE7XUB6}

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	2026-07-05T11:34:28.649543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca53117d57938a9bcb97022e927ef40f845790d02df37ac872665f32d6df669f

Aliases

arxiv: 2507.07076 · arxiv_version: 2507.07076v1 · doi: 10.48550/arxiv.2507.07076 · pith_short_12: ZJJRC7KXSOFJ · pith_short_16: ZJJRC7KXSOFJXS4X · pith_short_8: ZJJRC7KX

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/ZJJRC7KXSOFJXS4XAIXJE7XUB6 \
  | 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: ca53117d57938a9bcb97022e927ef40f845790d02df37ac872665f32d6df669f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a292766f82c22c4ef42ad93adac70d17f9d751a5ca29fb1d8ddedbea2c411fa",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-07-09T17:34:33Z",
    "title_canon_sha256": "9aa86150315b46293c5bf18dd737c1c44bfaced78a5bbb1977a2ee59528d2bd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07076",
    "kind": "arxiv",
    "version": 1
  }
}