Pith Number

pith:BKTKC7DV

pith:2014:BKTKC7DVJ7OD6S6CWYP2IXC5X2

not attested not anchored not stored refs pending

Duality and invariants of representations of fundamental groups of 3-manifolds into PGL(3,C)

Elisha Falbel, Qingxue Wang

arxiv:1412.7591 v2 · 2014-12-24 · 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{BKTKC7DVJ7OD6S6CWYP2IXC5X2}

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	2026-05-18T00:13:13.913143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aa6a17c754fdc3f4bc2b61fa45c5dbe8f7dd585a41c8d6159bd40eca0fb5b32

Aliases

arxiv: 1412.7591 · arxiv_version: 1412.7591v2 · doi: 10.48550/arxiv.1412.7591 · pith_short_12: BKTKC7DVJ7OD · pith_short_16: BKTKC7DVJ7OD6S6C · pith_short_8: BKTKC7DV

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/BKTKC7DVJ7OD6S6CWYP2IXC5X2 \
  | 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: 0aa6a17c754fdc3f4bc2b61fa45c5dbe8f7dd585a41c8d6159bd40eca0fb5b32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0396eb499c4a1a10e79caf17c984f324d62f49511ff1473385b802761e3a077",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-12-24T03:07:31Z",
    "title_canon_sha256": "cdca7e61736fb8e81e4369162a414b225831b892d926daec05a11f1c6e8580b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.7591",
    "kind": "arxiv",
    "version": 2
  }
}