Pith Number

pith:YQ5ANZRY

pith:2009:YQ5ANZRYMMCXEHXFUBXFCVFKQG

not attested not anchored not stored refs pending

On quasi-morphisms from knot and braid invariants

Michael Brandenbursky

arxiv:0907.2626 v4 · 2009-07-15 · math.GT · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YQ5ANZRYMMCXEHXFUBXFCVFKQG}

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	2026-05-18T03:52:12.701810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c43a06e6386305721ee5a06e5154aa81bd88ccc4dafe440b19876251c1d4432d

Aliases

arxiv: 0907.2626 · arxiv_version: 0907.2626v4 · doi: 10.48550/arxiv.0907.2626 · pith_short_12: YQ5ANZRYMMCX · pith_short_16: YQ5ANZRYMMCXEHXF · pith_short_8: YQ5ANZRY

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/YQ5ANZRYMMCXEHXFUBXFCVFKQG \
  | 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: c43a06e6386305721ee5a06e5154aa81bd88ccc4dafe440b19876251c1d4432d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d1235533f6a4c34c77b40c6b2f6f9bc9890d6d6e70c73a831ee3fef34e56349",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-07-15T15:35:55Z",
    "title_canon_sha256": "2a383130b8be4b7b92f01f4bcd7f9182c83f7ba6a0ed594b34e7beeb31b2f1d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2626",
    "kind": "arxiv",
    "version": 4
  }
}