Pith Number

pith:VWVYXF4S

pith:2016:VWVYXF4SEEYWKZAXR4DNWXQCRW

not attested not anchored not stored refs pending

Symmetric automorphisms of free groups, BNSR-invariants, and finiteness properties

Matthew C. B. Zaremsky

arxiv:1607.03043 v1 · 2016-07-11 · 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{VWVYXF4SEEYWKZAXR4DNWXQCRW}

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	2026-05-18T01:11:14.095173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adab8b979221316564178f06db5e028d83fcce08bc2f77979643b4b10f9c3dfb

Aliases

arxiv: 1607.03043 · arxiv_version: 1607.03043v1 · doi: 10.48550/arxiv.1607.03043 · pith_short_12: VWVYXF4SEEYW · pith_short_16: VWVYXF4SEEYWKZAX · pith_short_8: VWVYXF4S

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/VWVYXF4SEEYWKZAXR4DNWXQCRW \
  | 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: adab8b979221316564178f06db5e028d83fcce08bc2f77979643b4b10f9c3dfb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8599f106f13035a8aad471c3e8ba0d9188bc7576cbfa6f531406287ccf332d30",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-11T17:20:25Z",
    "title_canon_sha256": "2d89b2b9d5a0a7cfe4992ae920d25219d560a4fb227ec38c925ff800a7029174"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03043",
    "kind": "arxiv",
    "version": 1
  }
}