Phi, Fat, and the Mathematics of a Beautiful Midface
Bibliographic record
Abstract
PURPOSE: The Golden ratio, or Phi, has been used to explain the substrates of two-dimensional beauty utilizing the faces of models. A "Phi point" has been identified at the apex of the cheek mound that can be targeted in filler injections. The authors report herein how they have applied this algorithm for surgical shaping of the "beautiful" cheek as a routine part of their lower blepharoplasty procedure. The authors present their technique and results with patients undergoing lower blepharoplasty along with the adjunct of liposculpture to areas of volume deficiency in the midface with a particular goal of enhancing the Phi point. METHODS: This study was retrospective, consecutive, nonrandomized, interventional case series. The authors reviewed the medical records of 113 consecutive patients who underwent lower blepharoplasty with autologous fat transfer to the Phi point. The aesthetic outcome, patient satisfaction, and complication/revisions were evaluated. RESULTS: One hundred two out of 113 patients achieved excellent lower lid position and cheek enhancement as assessed by both patient and surgeon. In these 102 patients, there was significant improvement in lower lid appearance, contour, transition to the cheek, and cheek projection as observed by the surgeon. Three patients required revision to achieve sufficient volume. Eight patients were satisfied with the outcome, nevertheless, requested additional filler injection to optimize. CONCLUSIONS: Lower blepharoplasty combined with autologous fat transfer to reshape the Phi point is a safe and reliable technique and another step further in our quest for recreating the beautiful face.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".