Pith Number

pith:3BVKA2UH

pith:2026:3BVKA2UH5EX3EMK64UPZGG3GD5

not attested not anchored not stored refs resolved

Counting symmetric unimodular triangulations

J\"org Rambau, Kamillo Ferry, Michael Joswig

Lower and upper bounds are established for the number of symmetric unimodular triangulations of the dilated standard triangle with a fixed symmetry axis, along with complete enumerations for small cases.

arxiv:2605.14150 v1 · 2026-05-13 · math.CO · math.AG

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\pithnumber{3BVKA2UH5EX3EMK64UPZGG3GD5}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

Lower and upper bounds are given for symmetric unimodular triangulations with a fixed symmetry axis of the dilated standard triangle, along with full enumerations of small cases.

C2weakest assumption

The assumption that the symmetry is with respect to a fixed axis and that the triangulations are unimodular in the standard sense from the literature on T-curves.

C3one line summary

Bounds and enumerations for symmetric unimodular triangulations of dilated triangles are provided.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Rambau, J\"org , title =

[2] and Rambau, J\"org and Santos, Francisco , TITLE = 2010 · doi:10.1007/978-3-642-12971-1

[3] Orevkov, S. Yu. , TITLE =. J. Combin. Theory Ser. A , FJOURNAL =. 1999 , NUMBER =. doi:10.1006/jcta.1998.2921 , URL = 1999 · doi:10.1006/jcta.1998.2921

[4] Anclin, Emile E. , TITLE =. J. Combin. Theory Ser. A , FJOURNAL =. 2003 , NUMBER =. doi:10.1016/S0097-3165(03)00097-9 , URL = 2003 · doi:10.1016/s0097-3165(03)00097-9

[5] Aichholzer, Oswin and Hurtado, Ferran and Noy, Marc , TITLE =. Comput. Geom. , FJOURNAL =. 2004 , NUMBER =. doi:10.1016/j.comgeo.2004.02.003 , URL = 2004 · doi:10.1016/j.comgeo.2004.02.003

Receipt and verification

First computed	2026-05-17T23:39:11.589495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d86aa06a87e92fb2315ee51f931b661f6106f19a22204a38002cda57c340c4a0

Aliases

arxiv: 2605.14150 · arxiv_version: 2605.14150v1 · doi: 10.48550/arxiv.2605.14150 · pith_short_12: 3BVKA2UH5EX3 · pith_short_16: 3BVKA2UH5EX3EMK6 · pith_short_8: 3BVKA2UH

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/3BVKA2UH5EX3EMK64UPZGG3GD5 \
  | 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: d86aa06a87e92fb2315ee51f931b661f6106f19a22204a38002cda57c340c4a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49292a9ac7315221da2d506683b92354b1d649e68e1f806e380336bd64d4bfe8",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T22:04:57Z",
    "title_canon_sha256": "2f3646acecb5a3e05b1136152a8458eed4cb1532524f9ee4fcc69ded1ce11f79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14150",
    "kind": "arxiv",
    "version": 1
  }
}