Pith Number

pith:CTR73INU

pith:2020:CTR73INUOAJRNUMZY2Z4RBD7OT

not attested not anchored not stored refs pending

Pretzel knots up to nine crossings

P. M. G. Manch\'on, R. D\'iaz

arxiv:2011.09943 v1 · 2020-11-19 · 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{CTR73INUOAJRNUMZY2Z4RBD7OT}

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	2026-07-05T01:53:02.814690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14e3fda1b4701316d199c6b3c8847f74f7ef3482bdda337d2b6000c2a367c649

Aliases

arxiv: 2011.09943 · arxiv_version: 2011.09943v1 · doi: 10.48550/arxiv.2011.09943 · pith_short_12: CTR73INUOAJR · pith_short_16: CTR73INUOAJRNUMZ · pith_short_8: CTR73INU

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/CTR73INUOAJRNUMZY2Z4RBD7OT \
  | 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: 14e3fda1b4701316d199c6b3c8847f74f7ef3482bdda337d2b6000c2a367c649

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c80878f298d00a28746163e2cc319afb9fc55ad821d50aedd3c768527d0fdd14",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2020-11-19T16:30:07Z",
    "title_canon_sha256": "a4aa13a8ba7ea21bd4a74a0662e2678cb756fc338a48be46b1abe0a08cf85ace"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.09943",
    "kind": "arxiv",
    "version": 1
  }
}