Pith Number

pith:UMDGE6NP

pith:2026:UMDGE6NPJU2LDTUQQMOFIWEMGR

not attested not anchored not stored refs pending

Degree growth, orbit graphs, and functoriality for birational dynamical systems

Tomoyuki Takenawa

arxiv:2606.29274 v1 · 2026-06-28 · math.DS · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UMDGE6NPJU2LDTUQQMOFIWEMGR}

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	2026-06-30T01:17:59.922413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3066279af4d34b1ce90831c54588c3445f0d77f0576f9612dfd7f960069d39b

Aliases

arxiv: 2606.29274 · arxiv_version: 2606.29274v1 · doi: 10.48550/arxiv.2606.29274 · pith_short_12: UMDGE6NPJU2L · pith_short_16: UMDGE6NPJU2LDTUQ · pith_short_8: UMDGE6NP

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/UMDGE6NPJU2LDTUQQMOFIWEMGR \
  | 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: a3066279af4d34b1ce90831c54588c3445f0d77f0576f9612dfd7f960069d39b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8eb9291151d15d0d85a57a9360e62e6ec740530aee0f09917ff1e5c4e5a41a7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-28T08:43:50Z",
    "title_canon_sha256": "e2e15e373e0d913f08f63906bd24ec0fb82715390253089538bf5fec36019f95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29274",
    "kind": "arxiv",
    "version": 1
  }
}