Pith Number

pith:KGTV6OTJ

pith:2012:KGTV6OTJMJRQCGEKEFD3CDG7P4

not attested not anchored not stored refs pending

Twisted Alexander Invariants of Twisted Links

Daniel S. Silver, Susan G. Williams

arxiv:1202.1515 v1 · 2012-02-07 · 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{KGTV6OTJMJRQCGEKEFD3CDG7P4}

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	2026-05-18T04:02:53.166341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51a75f3a69626301188a2147b10cdf7f085bfc73f28a269c5f687948dcc8bb30

Aliases

arxiv: 1202.1515 · arxiv_version: 1202.1515v1 · doi: 10.48550/arxiv.1202.1515 · pith_short_12: KGTV6OTJMJRQ · pith_short_16: KGTV6OTJMJRQCGEK · pith_short_8: KGTV6OTJ

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/KGTV6OTJMJRQCGEKEFD3CDG7P4 \
  | 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: 51a75f3a69626301188a2147b10cdf7f085bfc73f28a269c5f687948dcc8bb30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b73ac2b644cbc0e2fad22ae36a4bb4af45dfbad9aa8437787ec0c31526e7ff35",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-02-07T20:26:14Z",
    "title_canon_sha256": "9b4ece91376c142c611bea920b82e9dc9bb454f4ba360f07f03ea10f5518e7d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.1515",
    "kind": "arxiv",
    "version": 1
  }
}