ICE HOCKEY - credits, sources, and the state of every number ============================================================ WHAT THIS IS ------------ An independent, self-contained reimplementation of the sport of ice hockey, written from published documents during a single build. It is not a port, a clone or a decompilation of any commercial hockey game: no code, art, audio, data or asset from any such game was used, examined or copied, and no league, team, crest, logo, player name or likeness appears anywhere in it. THERE IS NO ORIGINAL AUTHOR TO CREDIT, and that is unusual for a game. Ice hockey is a sport, not a work: it is older than any of its leagues and nobody owns it. What CAN be credited is the body that publishes the rules and the rink, and the researchers whose papers this app's physics is built on. Those are below, each with exactly what was taken from it. Original of the RINK AND THE RULES .... International Ice Hockey Federation (IIHF) Document ............................. IIHF Official Rule Book 2024/25, published 24 May 2024 Also used ............................ IIHF, Rules for Ice Rinks (older edition, undated) This reimplementation ................ written 2026-09-11, MIT licensed (LICENSE.txt) The two red-and-blue sweaters are red and blue because those colours were free. They are not any team's. The app uses the name "Ice Hockey" because that is the name of the sport. 1. SOURCES, WITH WHAT WAS TAKEN FROM EACH ----------------------------------------- S1 IIHF OFFICIAL RULE BOOK 2024/25 (PRIMARY - downloaded and read, 20,034,035 bytes, PDF 1.7, extracted with pdftotext -layout to 10,760 lines) https://blob.iihf.com/iihf-media/iihfmvc/media/contentimages/4_sport/officiating/rule_book/24_25/2024_iihf_rulebook_24052024_v1.pdf Taken: rule 1.2 rink size and corner radius; 1.3 board and glass heights; 1.5 goal, blue and centre line positions and widths; 1.7 officials' crease; 1.8 the goaltender's restricted trapezoid; 1.9 face-off spots, circles and hash marks; 2.1 the goal; 10.1 the stick's legal dimensions and blade curve; 13.1 the puck. S2 IIHF, RULES FOR ICE RINKS (PRIMARY - downloaded via web.archive.org, 182,922 bytes, 6 pages) http://www.iihf.com/education/Ice_Rink_Manual/IIHF_Rules_for_ice_rinks.pdf Taken: the statement that the ice between the goal lines is divided into three EQUAL parts - the word "equal" is in this edition and absent from the 2024/25 book; the goal frame's depth band 0.60 to 1.12 m; the crossbar's 5 cm external diameter. S4 WIKIPEDIA, "Ice hockey stick" (full plaintext via the MediaWiki API) https://en.wikipedia.org/wiki/Ice_hockey_stick Taken: the DEFINITION of the flex rating - "the amount of force (in pounds-force) that it takes to deflect or bend the shaft one inch" - the published range 40 to 160, the worked example "100 pounds-force (440 N)", the design formula F = 48 E I d / L^3, and the lie rule that a lie of 5 is a 135 degree angle with two degrees less per number. S5 A. VILLASENOR-HERRERA, "Recoil effect of the ice hockey stick during a slap shot", M.Sc. thesis, McGill University (PRIMARY - downloaded, 7,479,063 bytes, read with pdftotext) https://mcgill.scholaris.ca/bitstreams/2a0a10b8-ee95-403e-8966-63a4cd4ad9b1/download Taken directly: "An average stick stiffness of 15,000 N/m was assumed based on three point bend tests (Wu et al., 2003)"; the thesis's own regression V = 1.64 d + 19.73, r^2 = 0.82, N = 9; maximum shaft deflection 7.6 +- 4.0 degrees elite and 2.2 +- 1.5 recreational. Taken SECOND-HAND through it, and labelled so: Pearsall et al. (1999) four shaft stiffnesses 13, 16, 17 and 19 kN/m with puck speeds 108.2 and 105.9 km/h; Roy and Dore (1976) sticks at 17.1 and 24.1 lb/in; Wu et al. (2003) puck speeds 108 km/h slap and 70.92 km/h wrist. S6 I. FARKAS, G. BARTELS, T. UNGER and D. E. WOLF, "Frictional coupling between sliding and spinning motion", Phys. Rev. Lett. 90, 248302 (2003); arXiv:physics/0210024 (PRIMARY - LaTeX source downloaded from arxiv.org/e-print and read directly) Taken: the closed form for the dimensionless friction force and torque on a uniformly loaded sliding, spinning disk, in complete elliptic integrals; the eight published limiting values F(0)=0, F(1)=8/3pi, F'(1)=4/3pi, F(inf)=1, T(0)=2/3, T(1)=8/9pi, T'(1)=-4/3pi, T(inf)=0; and the central result that a disk "always stops its sliding and spinning motion at the same moment", with e -> e_0 ~= 0.653 "irrespective of the initial conditions". S7 J. M. J. VAN LEEUWEN, "Skating on slippery ice", SciPost Phys. 3, 042 (2017), arXiv:1706.08278v3, and "The friction of tilted skates on ice", SciPost Phys. 8, 059 (2020), arXiv:1910.13802v2 (PRIMARY - LaTeX sources downloaded and read) Taken: ice hardness p_H = (14.7 - 0.6 T) MPa, quoted there from Pourier et al., together with his own warning that "the value depends on the method of measurement"; Young's modulus of ice 0.88e9 Pa; "the order of magnitude of the friction coefficients is 0.002 for skating conditions"; the contact area estimate 14.3 mm^2; the lean relation tan(psi) = V^2 / (g R_c). Taken SECOND-HAND through him, and labelled so: de Koning, de Groot and van Ingen Schenau, J. Biomechanics 25 (1992) 565-571, "a friction force of 3.8 N for the straight strokes and 4.9 N for the curves" - the 1992 paper itself could NOT be reached (PubMed served a challenge page), so those two numbers are reported through van Leeuwen, not read at source. S8 M. PLESCH, J. PLESNIK and S. RUZICKOVA, "Influence of Physical Properties of Hockey Stick Blade on Shots", arXiv:1903.02635v2 (PRIMARY - LaTeX source downloaded and read) Taken: measured puck-on-blade friction coefficients 0.69 +- 0.02 (Specter sticker), 0.46 +- 0.07 (Renfrew tape longitudinal), 0.43 and 0.50 transverse; the wrist-shot contact "about 100 ms or more" and the slap-shot collision "certainly less than a millisecond"; puck energy "in the order of 100 Joules". Taken SECOND-HAND through it, and labelled so: Kays and Smith, Procedia Engineering 72 (2014) 563-568, doi 10.1016/j.proeng.2014.06.071 - the collision "accelerating the puck to about 60 % of its final speed". Elsevier returned 403 to every route tried, so that 60 % was never read at source. A WARNING recorded during the build: a guessed DOI for that paper (10.1016/j.proeng.2014.06.096) RESOLVES, with a 200, to a paper about snowboard edge grip. A 200 is not evidence; the correct DOI came from OpenAlex's title search. 2. A CORRECTION TO A PUBLISHED SOURCE ------------------------------------- The English Wikipedia article "Ice hockey rink" states that the blue lines are "15.0 metres (49.2 ft) (one quarter of the total length of the rink) apart" and cites the IIHF Official Rule Book 2024/25 above. THE CITED DOCUMENT DOES NOT SAY THAT. Rule 1.5 contains no 15.0 m figure and no fraction; it says the ice between the goals is divided into three zones, and the older IIHF ice rink document says those three parts are EQUAL. On a 60 m rink with the goal lines 4.0 m from each end, an equal zone is (60 - 8) / 3 = 17.3333 m, not 15.0 m. This app builds the equal-thirds rink and prints the disagreement on its own page. 3. A TYPO IN A PUBLISHED PAPER ------------------------------ The e >= 1 branch of the torque in Farkas et al. (S6), as printed in the arXiv LaTeX, is a factor of e^2 too small. Four independent things establish this: the paper's OWN stated derivative T'(1) = -4/3 pi, which the undisputed e <= 1 branch reproduces and the printed branch misses by more than a factor of two; a direct numerical quadrature of the paper's own defining integral; the app's engine, which computes the same physics a different way and was written first; and continuity at e = 1. The error survives a casual check because T(1), T(infinity) and even the paper's published fixed point e_0 = 0.653 are all invariant under it. The oracle in the build harness keeps the branch exactly as printed and carries the correction separately, because an oracle that quietly corrects its source is not an oracle. 4. EVERY NUMBER, BY STATE ------------------------- QUOTED - read out of a document named above. Rink 60 x 30 m, corner radius 8.5 m, boards 1.07 m, glass 2.4 m behind the goals and 1.8 m along the sides; goal lines 4.0 m from each end and 5 cm wide; blue and centre lines 30 cm wide; the centre spot 30 cm and the other spots 60 cm; every face-off circle 4.50 m; neutral-zone spots 1.50 m from the blue line and 14.0 m apart; hash marks 5 cm wide, 60 cm long, 1.70 m apart; officials' crease radius 3.0 m; trapezoid 6.80 m on the goal line and 8.60 m on the boards; goal 1.83 m by 1.22 m inside the posts, crossbar 5 cm; puck 76 mm by 25 mm, 156-170 g; stick 1.63 m (1.65 m for players 2.0 m and taller), blade 32 cm, blade width 50-76 mm, curve 19 mm max; flex range 40-160 and its definition; the lie rule; standard gravity 9.80665 m/s^2; the pound-force and the inch, both exact by definition. MEASURED - a published measurement, used as it stands. Puck-on-blade friction 0.46 and 0.69 (S8). Ice hardness (14.7 - 0.6 T) MPa and Young's modulus of ice 0.88 GPa (S7). The friction bracket 0.002 theory against 0.0054 and 0.0069 measured (S7, the measurements second-hand). Shaft stiffnesses 13-19 kN/m (S5, second-hand). Puck speeds 30.0 and 19.7 m/s (S5, second-hand). CALIBRATED - fitted so the model reproduces something published. THERE ARE EXACTLY TWO, and both are named on the app's own page. SWING_SLAP = 28.1131 m/s and SWING_WRIST = 20.5247 m/s, the hands' blade speed at contact, set so that the INTEGRATED puck speed comes out at the published 30.0 and 19.7 m/s. No published figure for the hands' own speed could be reached. Nothing downstream of these two is adjusted. RECONSTRUCTED - chosen by this app, because nobody publishes it. Every one of these appears in this list precisely so that it is never mistaken for a documented figure. Goal depth 0.90 m (inside the published 0.60-1.12 m band). End-zone face-off spots 6.0 m out from the goal line - the rulebook fixes them only in a picture. Goal crease: a 1.83 m arc with 1.22 m straight sides - likewise only in a picture. Skate blade 28 cm long, 3.0 mm wide, rocker radius 3.0 m, hollow radius 12.7 mm. A hockey blade is far shorter and far more rockered than the speed skate the ice-friction literature measures, and no hockey figure could be found. Shaft section 28.6 x 19.1 mm outside with a 2.0 mm wall, free span 1.524 m, stick mass 420 g, blade-plus-heel mass 130 g, laminate density 1550 kg/m^3. The modulus is then DERIVED from the flex number through the published definition, not chosen. Ice friction used: 0.0090 for a puck flat on the ice, 0.0060 along a blade. Both inside the published bracket. Across the blade the model uses a CONSTRAINT bounded at tan(60 degrees). Air drag: Cd 1.05 face-on and 0.80 on edge, air density 1.29 kg/m^3. Reconstructed from flat-plate and cylinder values; nothing hockey-specific was found. Restitution: 0.35 off the boards, 0.55 off a post, 0.30 off the ice. Pucks are frozen before play precisely to lower these and nobody publishes the numbers. Contact stiffness of the puck against the blade, derived from a 25 x 6 mm patch of vulcanised rubber at 60 MPa over 12 mm - a derivation from a chosen geometry, not a measurement. Skater mass 85 kg, peak leg force 900 N, peak leg power 1400 W, leg extension rate 2.5 m/s, stride 1.7 Hz, drag area 0.45 m^2, duty cycle 0.55, preferred splay 0.60 rad, maximum lean 60 degrees. Team size 5 skaters plus a goaltender; stick reach, goaltender reach and positioning, and every decision probability in the AI. The lead time of 11.5 ms between the blade leaving the ice and meeting the puck: derived as a quarter of the loaded shaft's first period, NOT fitted. The build harness reports that the fitted optimum would be about 16 ms and that shipping the derived figure costs 1.3 % of the shot. FALSIFIED - proposed during the build and disproved by the build's own harness, kept in the code so that it stays disproved. The yield-pressure bound on a skate edge's sideways bite. Written out with the published ice hardness it gives about 4 newtons where a leaning skater needs about 570, at every lean and every ice temperature tried. It is wrong by more than two orders of magnitude. 5. WHAT IS NOT MODELLED ----------------------- Body checking; penalties; offside and icing beyond the line test; the goaltender's equipment as separate colliding bodies; ice wear during a period; the temperature dependence of anything; and the pre-melt film physics that produces ice friction in the first place - the friction here is a coefficient with a disclosed bracket, not a hydrodynamic layer. A wrist shot is given the same one-millisecond collision as a slap shot, where the literature reports a hundred milliseconds of contact; the long push is not modelled, and the app says so on its own page. 6. SOFTWARE ----------- No third-party library of any kind is bundled. The renderer, the 4x4 matrix algebra, the beam integrator, the face-integral quadrature, the elliptic integrals in the build harness and the seeded generator (mulberry32) are all written for this app. Nothing is fetched from a network at run time. The app never calls a language model and can never spend a credit.