Pith Number

pith:77P2OZLH

pith:2016:77P2OZLHGKNQC4S4YJK6Y2ONNK

not attested not anchored not stored refs pending

Pure virtual braids, resonance, and formality

Alexander I. Suciu, He Wang

arxiv:1602.04273 v2 · 2016-02-13 · math.GR · 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{77P2OZLHGKNQC4S4YJK6Y2ONNK}

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	2026-05-18T00:40:14.010143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffdfa76567329b01725cc255ec69cd6ab555b45dd51f65223d0aa72de047dd99

Aliases

arxiv: 1602.04273 · arxiv_version: 1602.04273v2 · doi: 10.48550/arxiv.1602.04273 · pith_short_12: 77P2OZLHGKNQ · pith_short_16: 77P2OZLHGKNQC4S4 · pith_short_8: 77P2OZLH

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/77P2OZLHGKNQC4S4YJK6Y2ONNK \
  | 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: ffdfa76567329b01725cc255ec69cd6ab555b45dd51f65223d0aa72de047dd99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63467eb2535c0de65d662d8e73998100efafd7e0ca55021562bdefa7fdd735df",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-02-13T02:56:25Z",
    "title_canon_sha256": "7d9467d6337a6d69c75f6b1e741a382e75b5c5a77fe1e9a4ff51812c188074b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.04273",
    "kind": "arxiv",
    "version": 2
  }
}