Pith Number

pith:ECPHPOXJ

pith:2010:ECPHPOXJPDI6HD6TUMTAOT26FA

not attested not anchored not stored refs pending

Random length-spectrum rigidity for free groups

Ilya Kapovich

arxiv:1001.1729 v3 · 2010-01-12 · 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{ECPHPOXJPDI6HD6TUMTAOT26FA}

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	2026-05-18T04:30:03.844750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

209e77bae978d1e38fd3a326074f5e282e01cefce2422bcd6374d1380cb4fece

Aliases

arxiv: 1001.1729 · arxiv_version: 1001.1729v3 · doi: 10.48550/arxiv.1001.1729 · pith_short_12: ECPHPOXJPDI6 · pith_short_16: ECPHPOXJPDI6HD6T · pith_short_8: ECPHPOXJ

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/ECPHPOXJPDI6HD6TUMTAOT26FA \
  | 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: 209e77bae978d1e38fd3a326074f5e282e01cefce2422bcd6374d1380cb4fece

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "769c9d6f683a381a496533fbac9ec93268a320d4ba2b0caa152641974e93edc4",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-01-12T00:38:18Z",
    "title_canon_sha256": "a377a048b06eeb3d27f46da5db8bf3ecbe3f6fc2324c9959aa9404be481a733f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1729",
    "kind": "arxiv",
    "version": 3
  }
}