Pith Number

pith:4A4BPIG6

pith:2015:4A4BPIG6PPARBHXZOQHZ6WIXPX

not attested not anchored not stored refs pending

The minimum crossing number of essential tangles

Ant\'onio Salgueiro, Jo\~ao Miguel Nogueira

arxiv:1505.07268 v2 · 2015-05-27 · 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{4A4BPIG6PPARBHXZOQHZ6WIXPX}

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	2026-05-18T00:36:33.630940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e03817a0de7bc1109ef9740f9f59177de135a0a1e36dbf910191e45c2e589222

Aliases

arxiv: 1505.07268 · arxiv_version: 1505.07268v2 · doi: 10.48550/arxiv.1505.07268 · pith_short_12: 4A4BPIG6PPAR · pith_short_16: 4A4BPIG6PPARBHXZ · pith_short_8: 4A4BPIG6

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/4A4BPIG6PPARBHXZOQHZ6WIXPX \
  | 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: e03817a0de7bc1109ef9740f9f59177de135a0a1e36dbf910191e45c2e589222

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41e819163fbcaca7b0d19aa65d6f3ba6e322bc85ae6e3eb5070a8817116cdad5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-05-27T11:33:48Z",
    "title_canon_sha256": "e52617b31300ac10c7cd45f9b1b0278c5a473a607327f8e449c21c575ec490c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.07268",
    "kind": "arxiv",
    "version": 2
  }
}