Pith Number

pith:XN6UW5U7

pith:2017:XN6UW5U75VWGPNTGVWBTFPAVNY

not attested not anchored not stored refs pending

Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups

Michael Brandenbursky, Micha{\l} Marcinkowski

arxiv:1702.01662 v3 · 2017-02-06 · math.GT · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XN6UW5U75VWGPNTGVWBTFPAVNY}

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	2026-05-18T00:06:06.372455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb7d4b769fed6c67b666ad8332bc156e2aff393cd13cccaa18eab96280f22068

Aliases

arxiv: 1702.01662 · arxiv_version: 1702.01662v3 · doi: 10.48550/arxiv.1702.01662 · pith_short_12: XN6UW5U75VWG · pith_short_16: XN6UW5U75VWGPNTG · pith_short_8: XN6UW5U7

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/XN6UW5U75VWGPNTGVWBTFPAVNY \
  | 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: bb7d4b769fed6c67b666ad8332bc156e2aff393cd13cccaa18eab96280f22068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2ad7a7f9934a10da1f7fdbf3fef4d220e531dead769acfd2fa49c3d1577d58a",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-02-06T15:42:22Z",
    "title_canon_sha256": "8df1089ea3bc962f11087da0ff118c8cd952101f3e8559d6d52823962934ae2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.01662",
    "kind": "arxiv",
    "version": 3
  }
}