Venues as observers: the perceptual resolution of prediction markets

Working title: Two venues, one event, two quotes: a composed observation model for prediction-market prices, with pre-registered tests of crossing resolution curves

Author: [withheld in the repository copy]. Contact: [withheld].

Status: DRAFT. Revision: 2026-11-02 second sweep (related work, venues).

Every empirical result in this paper is DARK. The instrument exists, the corpus is being collected, and nothing has been scored. What is offered is a model, a measurement artifact, a fee geometry read from venue documentation, and a pre-registered evaluation plan that may return null.

Abstract (draft)

Two prediction-market venues quoting the same event often disagree, and the disagreement persists. The 2025–2026 studies agree the gaps are structural rather than informational, but none says what the structure is. We treat each venue as an observer of a latent probability π with its own perceptual apparatus, and write the quote as a composition of five operators: quote_v = Q∘B∘L∘W∘R(π). R is the referent (what the contract resolves on), W a probability weighting, L a lag, B the fee-induced no-trade band, and Q tick quantization. Each operator is estimable from its own data source: resolution text, calibration by horizon, trade timestamps, fee schedules, tick structures. Both venues charge fees proportional to p(1 − p), so the band is widest at p = 0.5; with venue-published parameters the two-leg cost at p = 0.50 is about 325 basis points, not the 40 an earlier design assumed; tail contracts are about five times cheaper. Because fee, tick and maker–taker asymmetry differ by venue, each venue has a perceptual resolution R_v(p), and we pre-register the falsifiable claim that the two curves cross, so any constant-weight fusion of the two quotes is misspecified. We also report a measurement artifact: a venue's own liquidity field is ask-side notional and ranks dead markets as deep. The inverted model will be scored by Brier and log loss on time-held-out resolved markets against each venue's raw quote and against single-operator debiasing. Every result is DARK; the fusion may return null, and null is a reportable outcome.

Contributions

1. The composed-operator observation model. quote_v = Q∘B∘L∘W∘R(π), with one data source per operator and a stated identifiability question: which operator absorbs which residual when the composite is inverted. Status: DESIGNED.
2. The fee geometry from venue documentation. Both venues' fees are ∝ p(1 − p). At p = 0.50 the two-leg cost is ~325 bps against 40 bps assumed by the earlier design (~9× more false "opportunities"); tails are ~5× cheaper (p = 0.50 → ~3.25¢; 0.10 → ~1.17¢; 0.05 → ~0.62¢). Kalshi rounds up to the cent, which dominates at small size; Polymarket US pays makers a rebate; Polymarket publishes an exponent on p(1 − p), observed 1. The code reads venue-published parameters and marks them "not authoritative, dated and sourced". Status: PINNED in fees.py tests.
3. The liquidity-field artifact. The venue's liquidity field is ask-side notional, (1 − p)·size collateral, so a p = 0.002 market with a 2.9M-contract resting sell scored $2.9M of "liquidity" against $735 of bids. depth_usd takes the minimum of the two sides within a band. Status: MEASURED.
4. Two pre-registered, falsifiable hypotheses with an evaluation plan. H1 (crossing): R_K(p) and R_P(p), defined as the smallest change in π that moves the venue's executable quote, cross at least once on (0, 1). H2 (fusion): the inverted-model π̂ beats the constant-weight average of the two quotes on Brier and log loss over time-held-out resolved markets; failure to beat is reported as such. Status: DESIGNED; results DARK.
5. A documented failed predecessor. The earlier "Autonomous Arbitrage Intelligence" design was removed because its spread took an absolute value, making a loss indistinguishable from a gain, and its "disparity D" score could never be wrong. Kept as a methods lesson on unfalsifiable scores. Status: HISTORY.
6. Abstention and coverage as first-class outputs. When referents fail alignment or the fee bands leave the two quote intervals disjoint, the fusion returns null, not a number; markets with no trades in a window are DARK, not zero.

Outline (≈ 7,000 words)

1. Dispersion is not disagreement (600 words). The 2024 election pair as the motivating case: Ng et al. (2025) find Polymarket leads Kalshi in price discovery; Clinton and Huang (2025) find identical contracts diverging across more than 2,500 markets; Gebele and Matthes (2026) find 2–4% execution-aware deviations across ten venues and attribute them to "structural frictions rather than informational disagreement". We take that attribution as the premise and ask what the frictions are, operator by operator.
2. A venue is an observer (800 words). The model and the metaphor made precise: a venue has a referent (R), a weighting (W), a lag (L), a band (B) and a grid (Q), and the quote is what survives all five. Manski (2006): a price only partially identifies belief. Ottaviani and Sørensen (2015): the price underreacts to information with heterogeneous priors. Satopää et al. (2014) as the log-odds measurement-error baseline the operator model generalizes.
3. Each operator, its literature, its data source (1,400 words). R: Gebele–Matthes semantic alignment; Nechepurenko's finality stages. W: Rothschild (2009) debiasing transform; Page and Clemen (2013) horizon dependence; Snowberg and Wolfers (2010) misperception over risk-love; Prelec (1998). L: Nechepurenko's joint price–age observation; Bandi, Pirino and Renò (2017) excess idle time. B: Constantinides (1986) and Dumas–Luciano (1991) no-trade regions; the venue fee schedules. Q: Harris (1991, 1994) discreteness; Manski and Molinari (2010) rounding as interval data; Dayri and Rosenbaum (2015) implicit spread.
4. Fee geometry and the crossing hypothesis (900 words). Polymarket: fee = C × feeRate × p × (1 − p), takers only, category feeRates 0 to 0.07 (official docs, read 2026-11-01 and re-read 2026-11-02: formula and rates unchanged, plus maker rebates of 20% Crypto, 15% Sports, 25% most other categories, 0% Combos, redistributed daily, and a Taker Rebate Program; still no tick size or date on the page). Kalshi: "fees = round up(0.07 x C x P x (1-P))", P the contract price in dollars, C the number of contracts, "round up = rounds to the next cent"; trading fees only on orders immediately matched (taker-only); no settlement or processing fee; S&P 500 and NASDAQ-100 index markets at 0.035 — PRIMARY from the 2022 CFTC-filed schedule, body extracted 2026-11-02. The live PDF ("Fee Schedule for July 2026 - 7.7.26 Update") is still unread (HTTP 429 on every fetch); its search-engine rendering shows a per-contract multiplier M on the 0.07 form and a 0.0175 formula for markets where the multiplier defaults to 0, both UNVERIFIED after search 2026-11-02. Kalshi Help (dated 19 Apr 2026) now charges maker fees on orders not immediately matched and varies fees per market, and Kalshi's fee-rounding doc replaces the next-cent round-up with ceil to $0.000001 plus a per-order rounding accumulator rebated at balance precision ($0.0001 direct members, $0.01 otherwise), so B and the quantization step inside it are estimated per fee regime. Tick structures: Kalshi publishes linear_cent, deci_cent and tapered variants finer at the edges; Polymarket's CLOB exposes minimum_tick_size. The structural argument: the band dominates at the centre and quantization at the edges, and venues differ on both, so R_K and R_P can cross. H1 as a test on realized spread-vs-price curves from order-book snapshots.
5. The liquidity artifact (400 words). What the field measures, why it inverts the ranking, and the depth_usd repair.
6. Pre-registered evaluation plan (1,100 words). (i) Freeze the venue-matching rule and the corpus manifest before pulling prices. (ii) Estimate operator parameters on a time-earlier window; score only markets resolving later (Rothschild's out-of-sample coefficient as precedent). (iii) Brier and log loss (Gneiting and Raftery 2007) plus recalibration slope by time-to-resolution bucket (Page–Clemen; Le 2026). (iv) Event-level clustering; report how much slope variation is noise (Le). (v) Baselines: each venue's raw quote; constant-weight average; Rothschild-style single-operator debiasing; Ranjan–Gneiting beta-transformed pool. (vi) Coverage stated; abstentions counted; null is an outcome.
7. The failed predecessor (400 words). Absolute-value spread; a score that cannot be wrong; why it was removed; what the current design does instead (signed, executable, scored against resolution).
8. Threats, what this is not, conclusion (400 words).

Related work and the negative space

Foundations. Wolfers and Zitzewitz (2004), J. Economic Perspectives 18(2), 107. Wolfers and Zitzewitz (2006), NBER WP 12200, conditions under which price ≈ mean belief. Manski (2006), Economics Letters 91(3), 425. Arrow et al. (2008), Science 320, 877. Hanson (2003), Information Systems Frontiers 5(1); Hanson (2007), J. Prediction Markets 1(1), 3. Chen and Pennock (2007), UAI 2007, 49; arXiv:1206.5252, the cost-function form of the LMSR (verified 2026-11-02). Snowberg, Wolfers and Zitzewitz (2013), Handbook of Economic Forecasting 2A. Page and Clemen (2013), Economic Journal 123(568), 491.

Favourite–longshot and weighting. Thaler and Ziemba (1988), J. Economic Perspectives 2(2), 161. Snowberg and Wolfers (2010), J. Political Economy 118(4), 723. Prelec (1998), Econometrica 66(3), 497. Ottaviani and Sørensen (2010), AEJ: Microeconomics 2(1), 58; Ottaviani and Sørensen (2015), American Economic Review 105(1), 1. Rothschild (2009), Public Opinion Quarterly 73(5), 895, the debiasing transform; its source, Leigh, Wolfers and Zitzewitz (2007), is verified as cited (Crossref's reference deposit for Rothschild 2009; the acknowledgment in Zitzewitz 2026) but its text is UNVERIFIED after search 2026-11-02. Zitzewitz (2026), NBER Working Paper 35846, "Are Prediction Markets Politically Biased?", DOI 10.3386/w35846.

Microstructure. Harris (1991), Review of Financial Studies 4(3), 389; Harris (1994), RFS 7(1), 149. Constantinides (1986), J. Political Economy 94(4), 842. Dumas and Luciano (1991), J. Finance 46(2), 577. Hasbrouck (1995), J. Finance 50(4), 1175, information shares. Gonzalo and Granger (1995), J. Business & Economic Statistics 13(1), 27. Dayri and Rosenbaum (2015), Market Microstructure and Liquidity 1(1). Bandi, Pirino and Renò (2017), Econometrica 85(6), 1793. Manski and Molinari (2010), JBES 28(2), 219, rounding as interval data. Leland (1985), J. Finance 40(5), 1283; Bensaid, Lesne, Pagès and Scheinkman (1992), Mathematical Finance 2(2), 63; Chao, Yao and Ye (2019), RFS 32(3), 1068: the finance neighbours for a cost-induced price interval on a binary claim (all verified at Crossref 2026-11-02); no source uses "no-trade band" for event contracts.

Cross-venue precedents. Franck, Verbeek and Nüesch (2010), Int. J. Forecasting 26(3), 448, bookmakers vs Betfair; Franck, Verbeek and Nüesch (2013), Economica 80(318), 300.

Combination and scoring. Satopää et al. (2014), Int. J. Forecasting 30(2), 344. Ranjan and Gneiting (2010), JRSS-B 72(1), 71: any linear pool of calibrated forecasts is uncalibrated. Gneiting and Raftery (2007), JASA 102(477), 359. Brier (1950), Monthly Weather Review 78(1), 1 (verified at Crossref 2026-11-02).

The 2025–2026 Kalshi–Polymarket layer. Ng, Peng, Tao and Zhou (2025), SSRN 5331995 (full text still unavailable, SSRN 403). Clinton and Huang (2025), SocArXiv, DOI 10.31235/osf.io/d5yx2_v1, 64 pp., read in full 2026-11-02. Gebele and Matthes (2026), arXiv:2601.01706. Nechepurenko (2026), arXiv:2610.00183, event finality; Nechepurenko (2026), SSRN 7581159, joint price–age observation on Kalshi. Le (2026), arXiv:2602.19520, calibration by domain across 429,000 contracts. Cardozo and Rivero-Wildemauwe (2026), arXiv:2609.12878, longshot bias on Polymarket. Portnaya (2026), arXiv:2606.19517, Polymarket vs option-implied binaries. Added 2026-11-02: Dubach (2026), arXiv:2604.24366, Polymarket order-book microstructure, quoted spread by mid-price decile. Fan, Sun and Zhao (2026), arXiv:2610.36639, occurrence versus timing in Polymarket prices. Nechepurenko (2026), arXiv:2609.16642, first and stable decidability on Kalshi. Zang, Andrade and Nakajima (2026), arXiv:2609.20017, CLOB and AMM coexisting on one event. Barot and Borkhatariya (2026), arXiv:2604.03888, confidence-weighted combination of market-implied probabilities with model consensus.

Negative space. Nearest neighbours and what they do not do. Each operator has a mature single-operator inversion: Rothschild inverts W alone; Manski–Molinari treat Q alone as interval data; Nechepurenko formalizes L and R and then explicitly stops short of cross-venue numerical comparison; Gebele–Matthes align R and conclude "structural frictions" without naming them; Constantinides and Dumas–Luciano give B in theory. No paper composes the five, estimates each from its own source, or asks which absorbs the residual. The term "perceptual resolution" appears in no abstract retrieved, and no source converts fee, tick and maker–taker asymmetry into an expressible-probability curve R_v(p), let alone compares two venues' curves; the nearest is Dubach (2026)'s Polymarket spread-by-price curve, one venue and no composition. Fees are nearly absent from the academic Kalshi–Polymarket abstracts; the full texts correct this (CORRECTION, second sweep below): four of the seven 2025–2026 papers carry fees as flat rates, flags or unvalued symbols, and Clinton–Huang describe them, but never as the p(1 − p) operator; the fee literature that notices the 50¢ peak is grey (Allium 2026). Ranjan–Gneiting prove constant-weight pooling is misspecified for calibrated forecasters, but we found no published study showing it on venue quotes (search scope: DARK) against held-out resolutions. No published fusion abstains; the nearest are Manski's partial identification and Nechepurenko's set-valued terminal observation.

Second sweep (2026-11-02). Fee documents. The Kalshi general fee form is now PRIMARY from the 2022 CFTC-filed schedule ("Kalshi Fee Schedule.docx", created 2022-09-09; body extracted locally): "fees = round up(0.07 x C x P x (1-P))", P the contract price in dollars, C the number of contracts, "round up = rounds to the next cent"; trading fees charged only on orders "immediately matched" (taker-only in 2022); "There is no settlement fee"; "There is no processing fee"; S&P 500 and NASDAQ-100 markets "round up(0.035 x C x P x (1-P))"; the fee-per-100-contracts table peaks at $1.75 at 50¢ and is mirror-symmetric down to $0.07 at 1¢ and 99¢, with the round-up floor making one contract cost $0.01 at P ≤ 0.15 or ≥ 0.85 and $0.02 between. The live PDF ("Fee Schedule for July 2026 - 7.7.26 Update") is still unread (HTTP 429 on three WebFetch attempts and one curl); its search-engine rendering shows a per-contract multiplier M on the 0.07 form and a second 0.0175 formula "for markets where the multiplier defaults to 0" — both UNVERIFIED after search 2026-11-02. Kalshi Help (dated 19 Apr 2026) says "Maker fees are charged for orders placed that are not immediately matched" and that some markets carry different fees, reversing the 2022 taker-only rule; Kalshi's fee-rounding doc replaces the next-cent round-up with "trade_fee = ceil_6dp(model_fee)" plus a per-order rounding accumulator rebated at the member's balance precision, so the quantization step inside B differs by period; the margin API's per-ticker maker/taker rates on notional show Kalshi now runs a second fee model beside p(1 − p). Polymarket's docs were re-read: formula ("fee = C × feeRate × p × (1 - p)"), "Only takers pay fees" and the category rates are unchanged; maker rebates 20% Crypto, 15% Sports, 25% most other categories, 0% Combos, redistributed daily; a Taker Rebate Program exists; still no tick size or date on the page. CORRECTION to the negative space above: fees do appear in four of the seven 2025–2026 full texts — Gebele–Matthes as a one-sided per-venue scalar δ(m) that lumps "platform fees, gas costs, tick-size constraints, and slippage" (Appendix Table 3: Kalshi "conservatively fixed at 1.5%", Polymarket CLOB 0%); Le §9.2 as a price-based fee-exposure measure from Kalshi's schedule (≈ 1.2–1.3¢ per contract, "so fees do not track the calibration differences"); Cardozo and Rivero-Wildemauwe as a market-level fee flag with returns before fees; Portnaya as fee parameters f_B + f_P in an additive friction term with half relative spreads — and descriptively in Clinton–Huang (Kalshi maximum 1.75% at $0.50; Polymarket ≈ $0.007 per trade; PredictIt 10% on profits plus 5% on withdrawal); never as the p(1 − p) operator. None of the seven separates fees, tick, lag, weighting and referent as operators, and none estimates a venue-specific R_v(p). Nearest per operator: Portnaya (additive fee + half-spread term; Proposition A.5, uniform tick noise of unstated width; backward merge to the latest Polymarket quote at or before the Binance timestamp; referent "close but not exact"); Gebele–Matthes δ(m) with a UTC standardization and a persistence filter for lag; Le's per-venue recalibration slopes by domain × horizon × size, with Polymarket trade timestamps carrying "approximately 3-hour noise" from Polygon block numbers; Cardozo's returns by price bin on one venue. Nearest resolution curve: Dubach (2026), arXiv:2604.24366, Polymarket median quoted spread by mid-price decile in basis points — 1,818 in the lowest decile, 400 across the middle, 53 in the highest, a "longshot spread premium" — from a 52-day WebSocket archive and a pre-registered 600-market panel; one venue, no fee or tick model, no composition, no crossing test; no Kalshi counterpart found. New verified entries: Zitzewitz (2026), NBER w35846; Fan, Sun and Zhao (2026), arXiv:2610.36639, decomposing log score and profit into occurrence and timing across 338 deadline ladders — about one eighth of the information in prices concerns timing, "a high price is therefore a sign that an event is likely rather than imminent", the first quantification of a referent component; Nechepurenko (2026), arXiv:2609.16642, first and stable decidability clocks on Kalshi, "an observability result, not a claim that no market was decidable"; Clinton and Huang (2025) in full, SocArXiv DOI 10.31235/osf.io/d5yx2_v1, 64 pp. dated 1 Dec 2025: cheapest-Harris plus cheapest-Trump across Kalshi, PredictIt and Polymarket closing prices below $1 on 62 of 65 days and growing in the last two weeks, the highest presidential cross-exchange daily-change correlation 0.19 (against 0.29 between logically incompatible margin contracts), and fn. 11 on UTC versus Eastern closing times; Zang, Andrade and Nakajima (2026), arXiv:2609.20017, CLOB and AMM coexisting on one event (screening rent, tail-demand rent), not fusion. The phrase "no-trade band" is used nowhere for binary contracts (an arXiv abstract search on fees, tick size and no-trade across 40 recent prediction-market papers returned no band, no no-trade region and no tick-quantization paper); the finance neighbours for a cost-induced price interval are Leland (1985), J. Finance 40, 1283; Bensaid, Lesne, Pagès and Scheinkman (1992), Math. Finance 2, 63; Chao, Yao and Ye (2019), RFS 32, 1068 (tick discreteness and fee-structure dispersion across venues; in Ng et al.'s reference list) — all verified at Crossref. Cross-venue fusion with heterogeneous noise is still absent; the nearest is Barot and Borkhatariya (2026), arXiv:2604.03888, a confidence-weighted Bayesian combination of market-implied probabilities with LLM-swarm consensus scored by Brier and log loss (market + model, not venue + venue). Brier (1950), MWR 78, 1, and Chen and Pennock (2007), UAI, 49, arXiv:1206.5252, are verified; Leigh, Wolfers and Zitzewitz (2007) is verified as cited (Crossref reference deposit of Rothschild 2009; the acknowledgment in w35846) but its text is UNVERIFIED after search 2026-11-02; Ng et al. (2025) remains SSRN-walled, so whether they use Hasbrouck information shares is unconfirmed (Hasbrouck 1995 is in their reference list). Four searches were refused by the session's search budget and are NOT RUN: the exact-title search for Leigh, Wolfers and Zitzewitz (2007); the Ng et al. PDF search; "no-trade region" … prediction market; Kalshi Polymarket "price discovery" "information share" OR "lead-lag" OR "Hasbrouck".

Evidence (from the dossier; every row carries its tier)

Claim	Pointer	Tier
Both venues charge fees ∝ p(1 − p) (theta·C·p·(1−p)), not flat; at p = 0.50 the two-leg cost is ~325 bps vs the 40 bps the original spec assumed (~9× more false "opportunities"); tails ~5× cheaper (p = 0.50 → ~3.25¢; 0.10 → ~1.17¢; 0.05 → ~0.62¢); Kalshi rounds up to the cent; Polymarket US pays makers a rebate; Polymarket publishes an exponent on p(1 − p), observed 1	AAI aai/economics/fees.py, tests/test_fees.py	PINNED (code reads venue-published parameters; "rates are not authoritative, dated and sourced")
The observation model quote_v = Q_v∘B_v∘L_v∘W_v∘R_v(π); each operator estimable from a different data source; the falsifiable core is that R_K(p) and R_P(p) cross so constant-weight fusion is misspecified	AAI README	DESIGNED
The venue's liquidity field is ask-side notional ((1 − p)·size collateral) and ranks the deadest markets as deepest: a p = 0.002 market with a 2.9M-contract resting sell scored $2.9M "liquidity" against $735 of bids; depth_usd uses the minimum of the two sides within a band	aai/research/microstructure.py	MEASURED (artifact found and documented)
The earlier "Autonomous Arbitrage Intelligence" design was removed: its spread took an absolute value (loss indistinguishable from gain) and its "disparity D" score could never be wrong	AAI README	HISTORY
Any Brier/log-loss result, any crossing of resolution curves, any fused-π skill	research/corpus_manifest.json (collection only)	DARK
The tool cannot trade: no exchange SDK, wallet, signing path or authentication	README	design property
Polymarket fee = C × feeRate × p × (1 − p), takers only, category rates 0–0.07; maker rebates 20% / 15% / 25% / 0% by category; a Taker Rebate Program	Polymarket docs, read 2026-11-01 and re-read 2026-11-02 (venue documentation, not the owner's measurement)	documentation
Kalshi general fee "fees = round up(0.07 x C x P x (1-P))", round up to the next cent, taker-only, index markets 0.035	2022 CFTC-filed schedule, body extracted 2026-11-02 (PRIMARY for 2022); the July-2026 PDF is unread (HTTP 429), so its multiplier form and 0.0175 variant are UNVERIFIED; Kalshi Help (19 Apr 2026) and the fee-rounding doc show maker fees and six-decimal rounding since	documentation (2022 PRIMARY; current schedule UNVERIFIED after search 2026-11-02)

DARK (do not type a number)

• Every Brier, log-loss and recalibration-slope result.
• Whether R_K and R_P cross, where, and how many times.
• Any skill of the fused π̂ over either venue or over constant weights.
• The size and half-life of Kalshi–Polymarket gaps in the owner's corpus.
• Abstention rate of the fusion.
• Number of matched markets in the corpus (manifest exists; not counted here).

Threats to validity

• Fee parameters are venue-published, dated, and change. Polymarket is reported (secondary) to have charged no trading fees through 2025 and rolled taker fees out on 2026-03-30; B differs by period and must be estimated per fee regime. The Kalshi 2022 form is now verified against the CFTC-filed primary; the July-2026 schedule is not (HTTP 429), Kalshi Help (19 Apr 2026) charges maker fees on resting orders and varies fees per market, and the rounding rule has moved from next-cent round-up to six-decimal ceilings with a per-order rebate, so the quantization step inside B also differs by period.
• Identifiability. Five composed operators inverted from one quote series: residuals can be pushed between W and B, or between L and R. The pre-registration must name the identifying assumptions and the data source that pins each operator.
• Referent alignment is the hardest operator. Nechepurenko argues cross-venue comparison is "blocked" until a semantic and calendar registry exists. A wrong match contaminates every downstream score; the matching rule is frozen before prices are pulled, and unmatched pairs are null.
• Selection into resolution. Scoring only resolved markets selects on outcome timing; horizon buckets and event clustering are mitigations, not cures.
• Sample size. Published samples now run to hundreds of thousands of contracts; a smaller corpus must justify itself by registration and out-of-sample design.
• Single researcher; cannot trade. The instrument never tests executability, so "false opportunities" is a model count, not a realized P&L.
• No peer-reviewed Kalshi–Polymarket study exists yet to anchor magnitudes; the layer is arXiv and SSRN.

What this paper is not

• Not a results paper. Every result is DARK until the registered plan runs.
• Not a trading strategy or an arbitrage study; the tool cannot trade, and executability is out of scope.
• Not a claim that one venue is "right"; both are observers of the same π with different apparatus.
• Not a psychophysics paper; "perceptual resolution" is a defined quantity (smallest change in π that moves the executable quote), not a claim about human perception.
• Not a replacement for Gebele–Matthes's alignment work; it depends on a referent-alignment step and names theirs as the nearest.