Pith Number

pith:ATACGMVE

pith:2010:ATACGMVEGR3HSBOXEI4FNUXJKS

not attested not anchored not stored refs pending

Constructing group actions on quasi-trees and applications to mapping class groups

Kenneth Bromberg, Koji Fujiwara, Mladen Bestvina

arxiv:1006.1939 v5 · 2010-06-10 · math.GR · 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{ATACGMVEGR3HSBOXEI4FNUXJKS}

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	2026-05-18T02:43:24.733391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04c02332a434767905d7223856d2e95492a07a410e433817076fef26958d1685

Aliases

arxiv: 1006.1939 · arxiv_version: 1006.1939v5 · doi: 10.48550/arxiv.1006.1939 · pith_short_12: ATACGMVEGR3H · pith_short_16: ATACGMVEGR3HSBOX · pith_short_8: ATACGMVE

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/ATACGMVEGR3HSBOXEI4FNUXJKS \
  | 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: 04c02332a434767905d7223856d2e95492a07a410e433817076fef26958d1685

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be5bc3855bcb1d18724f7f2a130610761ac038e3eb58b4efb68d4419e8aa57e0",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-10T02:02:43Z",
    "title_canon_sha256": "eba1e8cbe5b6b7dbaec642e146402dd945e2304966b4569491bf1f9d17770db2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.1939",
    "kind": "arxiv",
    "version": 5
  }
}