Pith Number

pith:ZXHDGK4B

pith:2019:ZXHDGK4BGSUWNICGCBSDIAILKZ

not attested not anchored not stored refs pending

Centralizers in Mapping Class Group and decidability of Thurston Equivalence

Kasra Rafi, Michael Yampolsky, Nikita Selinger

arxiv:1902.02645 v1 · 2019-02-05 · 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{ZXHDGK4BGSUWNICGCBSDIAILKZ}

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	2026-05-17T23:54:32.577306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdce332b8134a966a046106434010b5656b4ecfcc3db9e518e4d099a0b6f6036

Aliases

arxiv: 1902.02645 · arxiv_version: 1902.02645v1 · doi: 10.48550/arxiv.1902.02645 · pith_short_12: ZXHDGK4BGSUW · pith_short_16: ZXHDGK4BGSUWNICG · pith_short_8: ZXHDGK4B

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/ZXHDGK4BGSUWNICGCBSDIAILKZ \
  | 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: cdce332b8134a966a046106434010b5656b4ecfcc3db9e518e4d099a0b6f6036

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0fd9d5533b8c028e9f0fde080aa01434c526e330bd2572800082af246c126c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-02-05T20:20:30Z",
    "title_canon_sha256": "2818a1a6385b5fe49f02ad43fe0f36ecaeac82647dca38e93a1bf65d31fa06df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.02645",
    "kind": "arxiv",
    "version": 1
  }
}