Pith Number

pith:6AZ2TDGK

pith:2011:6AZ2TDGKMBACXTMEGXIUMATKR4

not attested not anchored not stored refs pending

Minimal pseudo-Anosov translation lengths on the complex of curves

Chia-Yen Tsai, Vaibhav Gadre

arxiv:1101.2692 v1 · 2011-01-13 · math.GT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6AZ2TDGKMBACXTMEGXIUMATKR4}

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	2026-05-18T02:22:57.690023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f033a98cca60402bcd8435d146026a8f06bf23447b5d350536d5ae8f191a1cd7

Aliases

arxiv: 1101.2692 · arxiv_version: 1101.2692v1 · doi: 10.48550/arxiv.1101.2692 · pith_short_12: 6AZ2TDGKMBAC · pith_short_16: 6AZ2TDGKMBACXTME · pith_short_8: 6AZ2TDGK

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/6AZ2TDGKMBACXTMEGXIUMATKR4 \
  | 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: f033a98cca60402bcd8435d146026a8f06bf23447b5d350536d5ae8f191a1cd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f295cf71f1ce36465c788b1cdf22f774e1c942746a41d7b8e30f1bd0b2f748db",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-01-13T23:34:58Z",
    "title_canon_sha256": "2dd2bcfdc966d03726d2d77e3acb73cb7575188673b7bac82fcd2da560118502"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2692",
    "kind": "arxiv",
    "version": 1
  }
}