Pith Number

pith:Q6N7UJZW

pith:2018:Q6N7UJZWDEOHH3IWBPL6YKKRBB

not attested not anchored not stored refs pending

Alexander- and Markov-type theorems for virtual trivalent braids

Abigayle Dirdak, Carmen Caprau, Erica Sawyer, Rita Post

arxiv:1804.09919 v2 · 2018-04-26 · 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{Q6N7UJZWDEOHH3IWBPL6YKKRBB}

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	2026-05-17T23:44:32.546646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

879bfa2736191c73ed160bd7ec295108412a9b3bf6465df7ae34db5da42b500c

Aliases

arxiv: 1804.09919 · arxiv_version: 1804.09919v2 · doi: 10.48550/arxiv.1804.09919 · pith_short_12: Q6N7UJZWDEOH · pith_short_16: Q6N7UJZWDEOHH3IW · pith_short_8: Q6N7UJZW

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/Q6N7UJZWDEOHH3IWBPL6YKKRBB \
  | 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: 879bfa2736191c73ed160bd7ec295108412a9b3bf6465df7ae34db5da42b500c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b95e6d17b34457192fd506ac512bcd49392de11e4bb988457fbd869432ebc17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-04-26T07:28:02Z",
    "title_canon_sha256": "1365f33ba25a6d5129893edc0bd82701c40e406a725c1009cb5fdee9de0e38d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.09919",
    "kind": "arxiv",
    "version": 2
  }
}