Pith Number

pith:ZMCUJUGQ

pith:2016:ZMCUJUGQBP56MT7K2IMWGMWYF4

not attested not anchored not stored refs pending

Twisted Alexander polynomials of hyperbolic links

Anh T. Tran, Takayuki Morifuji

arxiv:1606.06360 v3 · 2016-06-20 · 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{ZMCUJUGQBP56MT7K2IMWGMWYF4}

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	2026-05-18T01:01:41.927565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb0544d0d00bfbe64fead2196332d82f24591f494f4a7c9e73e7a87492814171

Aliases

arxiv: 1606.06360 · arxiv_version: 1606.06360v3 · doi: 10.48550/arxiv.1606.06360 · pith_short_12: ZMCUJUGQBP56 · pith_short_16: ZMCUJUGQBP56MT7K · pith_short_8: ZMCUJUGQ

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/ZMCUJUGQBP56MT7K2IMWGMWYF4 \
  | 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: cb0544d0d00bfbe64fead2196332d82f24591f494f4a7c9e73e7a87492814171

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "634d902891b7faf45b02d56f55c6f0b89046ef880efb9c7e23bfc6778a09c67a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-06-20T23:29:28Z",
    "title_canon_sha256": "5ac40357b030365ef87975b12684511a96e0b06c872634ba9ab2d2a812dfd53a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06360",
    "kind": "arxiv",
    "version": 3
  }
}