Pith Number

pith:WKPFMY6Q

pith:2016:WKPFMY6QATNHNRXEIEG7GB6UCF

not attested not anchored not stored refs pending

Alexander polynomial obstruction of bi-orderability for rationally homologically fibered knot groups

Tetsuya Ito

arxiv:1609.03673 v2 · 2016-09-13 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WKPFMY6QATNHNRXEIEG7GB6UCF}

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	2026-05-18T00:46:51.666409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b29e5663d004da76c6e4410df307d41165709ba85dfdacae7fa81c0bb4f35261

Aliases

arxiv: 1609.03673 · arxiv_version: 1609.03673v2 · doi: 10.48550/arxiv.1609.03673 · pith_short_12: WKPFMY6QATNH · pith_short_16: WKPFMY6QATNHNRXE · pith_short_8: WKPFMY6Q

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/WKPFMY6QATNHNRXEIEG7GB6UCF \
  | 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: b29e5663d004da76c6e4410df307d41165709ba85dfdacae7fa81c0bb4f35261

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d4391d263d6fcac2479de3d6b5e65b3264dee45c0e3fb5b8a1a1d40255d34fa",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-13T04:15:37Z",
    "title_canon_sha256": "769c466cd9ae10300d2e11566c62c5ed7d24421ae0b0f6b5aff3e8f8a109ccd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03673",
    "kind": "arxiv",
    "version": 2
  }
}