Pith Number

pith:FEY77WX3

pith:2011:FEY77WX3SPW73S5OH63XZT6Z65

not attested not anchored not stored refs pending

Spectral rigidity of automorphic orbits in free groups

Armando Martino, Ilya Kapovich, Mathieu Carette, Stefano Francaviglia

arxiv:1106.0688 v5 · 2011-06-03 · 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{FEY77WX3SPW73S5OH63XZT6Z65}

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	2026-05-18T02:32:54.677109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2931ffdafb93edfdcbae3fb77ccfd9f7738a261e3d957d8eb41f045de9c997bd

Aliases

arxiv: 1106.0688 · arxiv_version: 1106.0688v5 · doi: 10.48550/arxiv.1106.0688 · pith_short_12: FEY77WX3SPW7 · pith_short_16: FEY77WX3SPW73S5O · pith_short_8: FEY77WX3

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/FEY77WX3SPW73S5OH63XZT6Z65 \
  | 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: 2931ffdafb93edfdcbae3fb77ccfd9f7738a261e3d957d8eb41f045de9c997bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11513c296fbc52dd6e21c1f6e9e905d52fb0e306cd1b6e2e6bcbc41a509886d1",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-03T15:40:49Z",
    "title_canon_sha256": "940b039cbb2b93545d769c716dfaccd2402c5ee791cc99dcc2aa2a9bb7398220"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0688",
    "kind": "arxiv",
    "version": 5
  }
}