Pith Number

pith:SCAHJ6GD

pith:2026:SCAHJ6GD5HFEAHBI66RAKDPHHQ

not attested not anchored not stored refs pending

Parallel packing a square with isosceles right triangles and equilateral triangles

Chen-Yang Su

Any collection of equilateral triangles homothetic to a given one with total area at most √3/4 packs parallel into a unit square.

arxiv:2605.09406 v2 · 2026-05-10 · math.CO

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\usepackage{pith}
\pithnumber{SCAHJ6GD5HFEAHBI66RAKDPHHQ}

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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.

Claims

C1strongest claim

any collection of triangles homothetic to Δ, whose total area does not exceed √3/4, can be parallel packed into I. The upper bound of √3/4 is tight.

C2weakest assumption

All triangles are homothetic to the given equilateral triangle Δ with a side parallel to a side of the unit square, restricting them to parallel packing without individual rotations.

C3one line summary

Any collection of same-orientation equilateral triangles with total area ≤ √3/4 packs into a unit square, and the bound is tight.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-26T01:03:33.001094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

908074f8c3e9ca401c28f7a2050de73c328bb2044da2f3c25701b7c2a060fa59

Aliases

arxiv: 2605.09406 · arxiv_version: 2605.09406v2 · doi: 10.48550/arxiv.2605.09406 · pith_short_12: SCAHJ6GD5HFE · pith_short_16: SCAHJ6GD5HFEAHBI · pith_short_8: SCAHJ6GD

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/SCAHJ6GD5HFEAHBI66RAKDPHHQ \
  | 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: 908074f8c3e9ca401c28f7a2050de73c328bb2044da2f3c25701b7c2a060fa59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de5d08b937b906844f15242d3ba78c5322482e92350812ed64e5eeea1214c7dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-10T08:09:21Z",
    "title_canon_sha256": "eb0a23b3a1dd03251d0101fbd8b916faccad192060b43f65b7d25b3bad16e736"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09406",
    "kind": "arxiv",
    "version": 2
  }
}